SSAT Exam > SSAT Videos > Math > Basic Concepts of 3D Figures (Sphere & Hemisphere) - Mensuration
Basic Concepts of 3D Figures (Sphere & Hemisphere) - Mensuration Video
FAQs on Basic Concepts of 3D Figures (Sphere & Hemisphere) - Mensuration
| 1. What is the formula to calculate the surface area of a sphere? |  |
Ans. The formula to calculate the surface area of a sphere is 4πr^2, where r is the radius of the sphere.
| 2. How do you find the volume of a hemisphere? | |
Ans. To find the volume of a hemisphere, you can use the formula (2/3)πr^3, where r is the radius of the hemisphere.
| 3. Can the surface area of a hemisphere be greater than the surface area of a sphere? | |
Ans. No, the surface area of a hemisphere is always half the surface area of a sphere with the same radius. This is because a hemisphere is just half of a sphere.
| 4. What is the relationship between the volume of a hemisphere and the volume of a sphere? | |
Ans. The volume of a hemisphere is half the volume of a sphere with the same radius. This is because a hemisphere is just half of a sphere.
| 5. How can we differentiate between a sphere and a hemisphere? | |
Ans. A sphere is a three-dimensional figure that has all points on its surface equidistant from its center. On the other hand, a hemisphere is a half of a sphere, where the flat face is the base of the hemisphere and the curved surface is the rounded part.
Text Transcript from Video
so now we will see the next curve prefer
area volume and volume of the next 3d
figures that is sphere
so as we see like any as you see in this
very nice born I've seen the vault all
is actually a 3d cheater and it in the
form of sacrificial in the form of
circle so that's why did known as the
sphere so any this any clearer difficult
getting the shape of a ball is known as
fear like if you take the example of
Earth it is also in the spherically
shaving so all these are the spheres so
most important heed to find out the
curves of this area and the volume of
the spherical bottoms how to find out
the promise of this area is that it is a
square derivatives a circular part so
definitely trees having some radius so
to find out the total surface area of or
God surface area in this case token
service is always same as that of the
curved surface area so to find out the
work surface area of a sphere that this
formula which is known as 4 PI R square
this formula is used generally to find
out the total surface area or God
surface area of a spherical bodies and
to find out the volume of sphere that
will be equal to 4 by 3 pie r cube so
using these two formulas we can easily
find out the void volume curves of this
area of the spherical bodies then I
arielle denote the radius of the sphere
so by keeping the value of our we can if
you find out the volume rocks at this
area in the same way the next 3d figure
is Emma sphere hemispheric in the half
sphere practice is a sphere is cut in
between it's actually performs the
hemisphere
now you see the ball if you can move all
the cut between it has to these shapes
like a hemisphere or you can say the
ball to shave our bond is actually like
a hemisphere so in the case of
hemisphere again we need to find out the
cogs a space alien total surface area at
the bunch of Malta hemisphere so to find
out the total surface area or you can
say the curved surface area to find out
the curved surface area surface area
means this is the colored part of the
hemisphere so that is we need to find
out a surface area of this cow part so
when waddell how to find out the surface
area of the god part is just as idea of
this card called part is 2 PI R square
and if you need to find out the total
surface area of the semester mms here
then this includes this curved part plus
the circular a flat surface that is
there about them on the top of the
hemisphere this circular flat surface we
need to add the area of this circle of
grad surface to the surface area of
the hemisphere so as this is a circulant
part 2 definitely the area of the
circular part is PI R so it means a
curved surface area it is to buy r
square plus server pi i squared so this
will become 3 pie r square this is a
croton surface area of the hemisphere
now volume of the hemisphere SOS it is
the above the city or definitely volume
will okay off so volume of the
atmosphere will be due by the file are
you so these are the formula by look at
the end of the ridge we can easily find
out the total surface area code surface
area and the volume on the 3d figures so
now we see one of one of her some
examples on the baser ed can we see how
to solve that examples using these
formulas so first note down the example
three tubes I join
end-to-end
we
our side 5-centimeter so we need to find
out find the surface area
of the resulting cuboid so in the
question it is given that there are 3
q's is al join end to end so when three
cubes are joined Android and each group
size of site five sentiment last 3 q's
enjoyed end to it so definitely if we
join these three cubes it actually forms
a to boil and then SS forms a cuboid so
length of the cuboid will definitely
increase but the parents at height of
the cod fish soaked you will remain the
same so it means like I suppose there
are these three news
now there is an Una's second clue which
is just attached to this first few
gratis
you
so in this way these three tubes are
attached and ran to end so as these
three cubes are as asthma and went to
definitely their lens will increase so
it is actually formula Jew boy whose
length is increased but breads and i
hided are same as Delta Q so most
importantly we need to understand how
the figure of this accordingly we need
to realize like though if we are
attaching with cubes with the ends what
I mean what is increasing is land breads
or hi what do you need to take the
dimensions of the cuboid
so this is we got the figure when we
attach three tools so as you can see
that the channel irritated this has the
land take this as the breath and this as
the height so as you see the hydras
remains the same because as the three
cubes are attached to and so it is
actually forming a bunch big boy who's a
height is height is same that is this
part is here breadth is also same
birthday the length has increased as
each side is a 5 centimeter initially of
the tube so it's their language length
new length of the cuboid reading 15
centimeter red remains the same that is
5 centimeter and also height remains the
same that inspire section so in this way
if we we we have noted down the
dimensions are not guarding we need to
find out for surface area of the
resulting cuboid to find out the surface
area resulting to but if you see there
again this is the cuboid base is having
the sick surface so this runs our phase
having dimensions 15 in 25 so surface
area of the wrist front surface will be
obtained by it is 75 again it's bad
surface having a dimension 50 into so it
may I give the surface area of red part
will be 15 into x plus now again there
is top surface bottoms of fish or
dimensional top surface ar-15 and five
again because length is in damages or
length and height length is if you see
lenses 15 centimeter height is fine
sector so again the surface area of that
part will be 15 into x and similarly the
surface area of the bottom case will be
the pain in group 5 plus now the Octagon
there are two side faces and intercept
dimension of the side faces are five and
five so it means surface area of those
parts will be 5 into 5 plus 5 into 5 so
this is a surface area of the whole
resulting viewpoint so now if you kiss
always so we'll see who what will be the
answer so 15 in 25 will get 75 the same
way is 7
by four times will be added and then 500
525 two times will be added Sophie are
at all this you get 3 50 centimeter
square is the answer so this is a
surface area of the whole the jetting
cuboid is made when three cubes are
joined end to end at each use as a side
of 5 centimeter so as this three tubes
are joined to definitely response to boy
whose length is increased but brats and
hydroxy so buddy we we have seen the
dimensions of this is articulate and
accordingly be my outer surface area is
resulting cuboid so now we move on to
the next example first right on the
cushion it is from a solid circular
cylinder
with high
10 centimeter and radius of the case is
600
so a right circular
cool Oh same time and same regis for
Cindy's
is removed find the volume of the
remaining
solid and also find
the total surface area so in the
question it is given that there is a
right circular cylinder which oocyte is
given as 10 centimeter and radius of the
base is given as 6 second and from
direct cylinder a right circular cone of
a game same height and same base is
removed is removable so accordingly we
need to find out the volume of the
remaining solid also need to find out
the total surface area so first we will
see first we'll see how you work however
the figure of this cushion information
given that is given what we really first
drawn to figure selvamani it is easier
for us to understand push and hopefully
end to swallow cushion so any it is
given that this is the cylinder whose
height is given as 10 centimeter and
radius of this base is given as 6
centimeters now the code is cut of the
same base that is having the same radius
and same height coal is correct
so this is the bone which is actually
down from the cylinder having the same
base and same height so accordingly we
need to find out the volume of the
remaining part and the total surface
area of the remaining part so how you
find out the gophers we need to find out
the volume so now to find out the volume
of the remaining
see initially there is a cylinder if you
cut down the phone from the cylinder
that they will it means like we have
occurred down the volume of the phone
from the bottom of the cylinder so as we
have removed the volume of the phone
from the volume of cylinder the
remaining part accordingly believe we
can solve this all sufficient and
accordingly we can find out the volume
of the remaining part that means we have
to read out the volume of the phone from
the volume of cylinder to find out the
volume of the remaining but so how to
solve it is first we see it means one of
us will write down this part this thing
that is volume of the remaining part is
equal to volume cylinder minus one new
phone so first we see what we do the
volume of cylinder and volume of bone
and accordingly we return then find out
the volume of the remaining part so
volume of cylinder as we have seen as we
know the formula for finding out the
body is PI R square h minus volume of
the bone volume of bone is 1 by 35 R
squared H so now if you solve it what we
garden as you can see that the water in
the case of 10 cylinder and forth about
the radius of the cylinder and cone is
same and I also the height of cylinder
and bore is seen so that's why we have
taken both as r and h so now if you
solid will get 2 by 3 pie r square H so
now we will keep the value of r & edge
here and we'll try to solder 2 by 3 pi
if by as it is r square edge so r square
field as we entered re 6 centimeter so
it means 6 square it wet and edge is
given as 10 centimeter so we are kept
value of H Norman solid is 2 by 3 into
pi into 6 square that is 26 into 10 we
can cancel out this strategy
from they will react well here so it we
spoon to buy into dwelling good answer
to 45 centimeter cube so this is the
volume of them volume of the remaining
part that we burn that is from the
volume of the cylinder we have deducted
the ornament of course so when you
record the volume of the remaining part
that is 245 between you want me and keep
the value of x also and we can solve it
also and now the second part of
the question says that we need to also
find out that total surface area so for
pending order totals and they say what
we need to do is protons the face area
watching in what we need to do is if we
observe this figure that definitely
there is a God surface part of them
cylinder and there is a definitely the
surface a surface area of the bottom one
cylinder also but top the cylinder is a
blank because we have cut it on the cone
from there but definitely there is a
inner part of the cylinder which is
actually the home so it means we need to
find out the curved surface area on this
phone which is this part then which is
actually the inner part of the cylinder
and we have to add this a god surface
area of the phone to rock surface area
of the cylinder plus surface area of the
base so accordingly we can find out the
total surface area of the remaining part
so for finding or approval surface area
first you see the curve surface area of
the cylinder as we noted record surface
area of the cylinder is 2 pi r h plus we
need to add the surface area of the
bottom of the cylinder is PI R square
plus now the gods surface area of the
phone which is actually the inner part
of the selector we need to add that part
also because we need to find our local
surface area which includes it's a
surface area of the outer and the inner
body so that is called surface area of
the pony so God surface area of the
phone as we know is pi r n no Vicki will
keep the value of all existing and
accordingly
find out the total surface area so 2
into pi which we keep by as it is r is
as we know that a sense an edge is 10
plus pi r is 6 so 6 square plus pi into
our is 6 into le so now we need to find
out the value of n lv know exactly the
curved surface area for binding on the
sorry L is actually the slant height so
for finding out the slant height what we
need to do is we have seen how to find
out the slant hydrant is elsewhere equal
s square plus i square but now as we
noted the value of H & R so refer do you
keep the value of the edge and RB and we
find out the value of L that is l square
is equal to edge is given as 10 shift
ends where those r is given as 6 so 6
square so l square is equal to 10 square
plus 6 squared at 150 lat 136 so l is
equal to under root 1 9 36 so this is
the value of L be bought so but you will
keep the value of L yeah that is pi RL
that is wonder whose 146 now we try to
solve it is you take the pie common so
cutting will get the true inducing
status were 1 22 10 went to 1600 is 120
plus 36 36 square plus 6 into one every
six under root 1 honey singh so 6 into
10 126 now in further solid take the pie
common one brandy glass surfaces you get
one group is plus now if you solve this
undergo part or that is under 130
suspected it is your cat l is equal
under root 1 gotta see this she solid
hard bottle radius we take the first
factors of what a disease of 100 factors
of water physics are factors of under
this is a courtesy so these are the
factors of under quantities we can also
take the pattern of 34 @ is go to 70 but
we are not taking
because if we see here that there is
only one here of one carries 400 his of
two and if you take the practice of 34
today stewards are no clear song to and
17 there so that's why we have not taken
the doctor of 34 so it will be coming as
the mayor of response or eating poo
outside circle to come to route 54 and
we're right down here it is six into to
route 24 that is 2 l root countries for
so this is the answer gratis sentiment
atmosphere so this is the total surface
area of the remaining part that is that
is we are cutting on the fone bone from
the cylinder so the remaining part we've
got so this is this way we can find out
the total surface area of the demeaning
part and if you want to put the solid
like we move on to keep the value of pi
year you can keep the value of pi and
according we can further solid but it is
not necessary that you always always
keep the fire focus on it so if you keep
it miss you all so it's also the right
and accordingly this is the answer of
the total surface area at the volume of
the remaining part so here again we have
used the formula for the volume of the
cylinder volume of the for what surface
40 count surface area of the cylinder
and surface area of the phone to
find out the total surface area as well
as the volume of the remaining part
area volume and volume of the next 3d
figures that is sphere
so as we see like any as you see in this
very nice born I've seen the vault all
is actually a 3d cheater and it in the
form of sacrificial in the form of
circle so that's why did known as the
sphere so any this any clearer difficult
getting the shape of a ball is known as
fear like if you take the example of
Earth it is also in the spherically
shaving so all these are the spheres so
most important heed to find out the
curves of this area and the volume of
the spherical bottoms how to find out
the promise of this area is that it is a
square derivatives a circular part so
definitely trees having some radius so
to find out the total surface area of or
God surface area in this case token
service is always same as that of the
curved surface area so to find out the
work surface area of a sphere that this
formula which is known as 4 PI R square
this formula is used generally to find
out the total surface area or God
surface area of a spherical bodies and
to find out the volume of sphere that
will be equal to 4 by 3 pie r cube so
using these two formulas we can easily
find out the void volume curves of this
area of the spherical bodies then I
arielle denote the radius of the sphere
so by keeping the value of our we can if
you find out the volume rocks at this
area in the same way the next 3d figure
is Emma sphere hemispheric in the half
sphere practice is a sphere is cut in
between it's actually performs the
hemisphere
now you see the ball if you can move all
the cut between it has to these shapes
like a hemisphere or you can say the
ball to shave our bond is actually like
a hemisphere so in the case of
hemisphere again we need to find out the
cogs a space alien total surface area at
the bunch of Malta hemisphere so to find
out the total surface area or you can
say the curved surface area to find out
the curved surface area surface area
means this is the colored part of the
hemisphere so that is we need to find
out a surface area of this cow part so
when waddell how to find out the surface
area of the god part is just as idea of
this card called part is 2 PI R square
and if you need to find out the total
surface area of the semester mms here
then this includes this curved part plus
the circular a flat surface that is
there about them on the top of the
hemisphere this circular flat surface we
need to add the area of this circle of
grad surface to the surface area of
the hemisphere so as this is a circulant
part 2 definitely the area of the
circular part is PI R so it means a
curved surface area it is to buy r
square plus server pi i squared so this
will become 3 pie r square this is a
croton surface area of the hemisphere
now volume of the hemisphere SOS it is
the above the city or definitely volume
will okay off so volume of the
atmosphere will be due by the file are
you so these are the formula by look at
the end of the ridge we can easily find
out the total surface area code surface
area and the volume on the 3d figures so
now we see one of one of her some
examples on the baser ed can we see how
to solve that examples using these
formulas so first note down the example
three tubes I join
end-to-end
we
our side 5-centimeter so we need to find
out find the surface area
of the resulting cuboid so in the
question it is given that there are 3
q's is al join end to end so when three
cubes are joined Android and each group
size of site five sentiment last 3 q's
enjoyed end to it so definitely if we
join these three cubes it actually forms
a to boil and then SS forms a cuboid so
length of the cuboid will definitely
increase but the parents at height of
the cod fish soaked you will remain the
same so it means like I suppose there
are these three news
now there is an Una's second clue which
is just attached to this first few
gratis
you
so in this way these three tubes are
attached and ran to end so as these
three cubes are as asthma and went to
definitely their lens will increase so
it is actually formula Jew boy whose
length is increased but breads and i
hided are same as Delta Q so most
importantly we need to understand how
the figure of this accordingly we need
to realize like though if we are
attaching with cubes with the ends what
I mean what is increasing is land breads
or hi what do you need to take the
dimensions of the cuboid
so this is we got the figure when we
attach three tools so as you can see
that the channel irritated this has the
land take this as the breath and this as
the height so as you see the hydras
remains the same because as the three
cubes are attached to and so it is
actually forming a bunch big boy who's a
height is height is same that is this
part is here breadth is also same
birthday the length has increased as
each side is a 5 centimeter initially of
the tube so it's their language length
new length of the cuboid reading 15
centimeter red remains the same that is
5 centimeter and also height remains the
same that inspire section so in this way
if we we we have noted down the
dimensions are not guarding we need to
find out for surface area of the
resulting cuboid to find out the surface
area resulting to but if you see there
again this is the cuboid base is having
the sick surface so this runs our phase
having dimensions 15 in 25 so surface
area of the wrist front surface will be
obtained by it is 75 again it's bad
surface having a dimension 50 into so it
may I give the surface area of red part
will be 15 into x plus now again there
is top surface bottoms of fish or
dimensional top surface ar-15 and five
again because length is in damages or
length and height length is if you see
lenses 15 centimeter height is fine
sector so again the surface area of that
part will be 15 into x and similarly the
surface area of the bottom case will be
the pain in group 5 plus now the Octagon
there are two side faces and intercept
dimension of the side faces are five and
five so it means surface area of those
parts will be 5 into 5 plus 5 into 5 so
this is a surface area of the whole
resulting viewpoint so now if you kiss
always so we'll see who what will be the
answer so 15 in 25 will get 75 the same
way is 7
by four times will be added and then 500
525 two times will be added Sophie are
at all this you get 3 50 centimeter
square is the answer so this is a
surface area of the whole the jetting
cuboid is made when three cubes are
joined end to end at each use as a side
of 5 centimeter so as this three tubes
are joined to definitely response to boy
whose length is increased but brats and
hydroxy so buddy we we have seen the
dimensions of this is articulate and
accordingly be my outer surface area is
resulting cuboid so now we move on to
the next example first right on the
cushion it is from a solid circular
cylinder
with high
10 centimeter and radius of the case is
600
so a right circular
cool Oh same time and same regis for
Cindy's
is removed find the volume of the
remaining
solid and also find
the total surface area so in the
question it is given that there is a
right circular cylinder which oocyte is
given as 10 centimeter and radius of the
base is given as 6 second and from
direct cylinder a right circular cone of
a game same height and same base is
removed is removable so accordingly we
need to find out the volume of the
remaining solid also need to find out
the total surface area so first we will
see first we'll see how you work however
the figure of this cushion information
given that is given what we really first
drawn to figure selvamani it is easier
for us to understand push and hopefully
end to swallow cushion so any it is
given that this is the cylinder whose
height is given as 10 centimeter and
radius of this base is given as 6
centimeters now the code is cut of the
same base that is having the same radius
and same height coal is correct
so this is the bone which is actually
down from the cylinder having the same
base and same height so accordingly we
need to find out the volume of the
remaining part and the total surface
area of the remaining part so how you
find out the gophers we need to find out
the volume so now to find out the volume
of the remaining
see initially there is a cylinder if you
cut down the phone from the cylinder
that they will it means like we have
occurred down the volume of the phone
from the bottom of the cylinder so as we
have removed the volume of the phone
from the volume of cylinder the
remaining part accordingly believe we
can solve this all sufficient and
accordingly we can find out the volume
of the remaining part that means we have
to read out the volume of the phone from
the volume of cylinder to find out the
volume of the remaining but so how to
solve it is first we see it means one of
us will write down this part this thing
that is volume of the remaining part is
equal to volume cylinder minus one new
phone so first we see what we do the
volume of cylinder and volume of bone
and accordingly we return then find out
the volume of the remaining part so
volume of cylinder as we have seen as we
know the formula for finding out the
body is PI R square h minus volume of
the bone volume of bone is 1 by 35 R
squared H so now if you solve it what we
garden as you can see that the water in
the case of 10 cylinder and forth about
the radius of the cylinder and cone is
same and I also the height of cylinder
and bore is seen so that's why we have
taken both as r and h so now if you
solid will get 2 by 3 pie r square H so
now we will keep the value of r & edge
here and we'll try to solder 2 by 3 pi
if by as it is r square edge so r square
field as we entered re 6 centimeter so
it means 6 square it wet and edge is
given as 10 centimeter so we are kept
value of H Norman solid is 2 by 3 into
pi into 6 square that is 26 into 10 we
can cancel out this strategy
from they will react well here so it we
spoon to buy into dwelling good answer
to 45 centimeter cube so this is the
volume of them volume of the remaining
part that we burn that is from the
volume of the cylinder we have deducted
the ornament of course so when you
record the volume of the remaining part
that is 245 between you want me and keep
the value of x also and we can solve it
also and now the second part of
the question says that we need to also
find out that total surface area so for
pending order totals and they say what
we need to do is protons the face area
watching in what we need to do is if we
observe this figure that definitely
there is a God surface part of them
cylinder and there is a definitely the
surface a surface area of the bottom one
cylinder also but top the cylinder is a
blank because we have cut it on the cone
from there but definitely there is a
inner part of the cylinder which is
actually the home so it means we need to
find out the curved surface area on this
phone which is this part then which is
actually the inner part of the cylinder
and we have to add this a god surface
area of the phone to rock surface area
of the cylinder plus surface area of the
base so accordingly we can find out the
total surface area of the remaining part
so for finding or approval surface area
first you see the curve surface area of
the cylinder as we noted record surface
area of the cylinder is 2 pi r h plus we
need to add the surface area of the
bottom of the cylinder is PI R square
plus now the gods surface area of the
phone which is actually the inner part
of the selector we need to add that part
also because we need to find our local
surface area which includes it's a
surface area of the outer and the inner
body so that is called surface area of
the pony so God surface area of the
phone as we know is pi r n no Vicki will
keep the value of all existing and
accordingly
find out the total surface area so 2
into pi which we keep by as it is r is
as we know that a sense an edge is 10
plus pi r is 6 so 6 square plus pi into
our is 6 into le so now we need to find
out the value of n lv know exactly the
curved surface area for binding on the
sorry L is actually the slant height so
for finding out the slant height what we
need to do is we have seen how to find
out the slant hydrant is elsewhere equal
s square plus i square but now as we
noted the value of H & R so refer do you
keep the value of the edge and RB and we
find out the value of L that is l square
is equal to edge is given as 10 shift
ends where those r is given as 6 so 6
square so l square is equal to 10 square
plus 6 squared at 150 lat 136 so l is
equal to under root 1 9 36 so this is
the value of L be bought so but you will
keep the value of L yeah that is pi RL
that is wonder whose 146 now we try to
solve it is you take the pie common so
cutting will get the true inducing
status were 1 22 10 went to 1600 is 120
plus 36 36 square plus 6 into one every
six under root 1 honey singh so 6 into
10 126 now in further solid take the pie
common one brandy glass surfaces you get
one group is plus now if you solve this
undergo part or that is under 130
suspected it is your cat l is equal
under root 1 gotta see this she solid
hard bottle radius we take the first
factors of what a disease of 100 factors
of water physics are factors of under
this is a courtesy so these are the
factors of under quantities we can also
take the pattern of 34 @ is go to 70 but
we are not taking
because if we see here that there is
only one here of one carries 400 his of
two and if you take the practice of 34
today stewards are no clear song to and
17 there so that's why we have not taken
the doctor of 34 so it will be coming as
the mayor of response or eating poo
outside circle to come to route 54 and
we're right down here it is six into to
route 24 that is 2 l root countries for
so this is the answer gratis sentiment
atmosphere so this is the total surface
area of the remaining part that is that
is we are cutting on the fone bone from
the cylinder so the remaining part we've
got so this is this way we can find out
the total surface area of the demeaning
part and if you want to put the solid
like we move on to keep the value of pi
year you can keep the value of pi and
according we can further solid but it is
not necessary that you always always
keep the fire focus on it so if you keep
it miss you all so it's also the right
and accordingly this is the answer of
the total surface area at the volume of
the remaining part so here again we have
used the formula for the volume of the
cylinder volume of the for what surface
40 count surface area of the cylinder
and surface area of the phone to
find out the total surface area as well
as the volume of the remaining part
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Apr 19, 2026 Last updated
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