Points to Remember: Surface Areas & Volumes | Mathematics (Maths) Class 10 PDF Download

 Page 1


Surface Areas 
 and  
Volumes 
Page 2


Surface Areas 
 and  
Volumes 
Total Surface Area (2D) Shape
Lateral/ Curved
Surface Area
p r r (   + l )
2lb + 2bh + 2lh 2(l + b) x h
4 p r
2
3 p r
2
2 p r
2
4 pr
2
2 pr
2
p r h
2
p
r h
2
3
1 _
4
p r
3
_
3
2
p r
3
_
3
6
2
l 4
2
l
Volume (3D)
lbh
Cube
Sphere
Diagonal of Cuboid        ;      Slant height of Cone (l )          ;       Slant height of Frustum (l )
Surface Area: It is the sum of the total exposed area of a three dimensional solid object. It’s unit can be cm
2
, m
2
 etc.
Volume:    It is the amount of space occupied by an object. It’s unit can be cm
3
, m
3
, etc.
Cuboid
Cylinder
Frustum
Hemisphere
Cone
pr
r h (         ) 2
 + prh 2
prl
pl (R + r)
p r r r r
3
1 _
(                       )
2
1 1 2 2
2
h + +
1 2
p p r r
r r
(           )
(            ) l     
2
1 2
2
+
+ +
l
3
r
h
l b
h
l
l l
r
h
r1
r2
h
l
r
o
r
o
 
(Solid)
(Hollow)
=   l 
2
 + b
2
 + h
2
=    h
2
 + r
2
=    h
2
 + (r
1
 - r
2
)
2
Surface Areas & Volumes
SURFACE AREAS & VOLUMES
Page 3


Surface Areas 
 and  
Volumes 
Total Surface Area (2D) Shape
Lateral/ Curved
Surface Area
p r r (   + l )
2lb + 2bh + 2lh 2(l + b) x h
4 p r
2
3 p r
2
2 p r
2
4 pr
2
2 pr
2
p r h
2
p
r h
2
3
1 _
4
p r
3
_
3
2
p r
3
_
3
6
2
l 4
2
l
Volume (3D)
lbh
Cube
Sphere
Diagonal of Cuboid        ;      Slant height of Cone (l )          ;       Slant height of Frustum (l )
Surface Area: It is the sum of the total exposed area of a three dimensional solid object. It’s unit can be cm
2
, m
2
 etc.
Volume:    It is the amount of space occupied by an object. It’s unit can be cm
3
, m
3
, etc.
Cuboid
Cylinder
Frustum
Hemisphere
Cone
pr
r h (         ) 2
 + prh 2
prl
pl (R + r)
p r r r r
3
1 _
(                       )
2
1 1 2 2
2
h + +
1 2
p p r r
r r
(           )
(            ) l     
2
1 2
2
+
+ +
l
3
r
h
l b
h
l
l l
r
h
r1
r2
h
l
r
o
r
o
 
(Solid)
(Hollow)
=   l 
2
 + b
2
 + h
2
=    h
2
 + r
2
=    h
2
 + (r
1
 - r
2
)
2
Surface Areas & Volumes
SURFACE AREAS & VOLUMES
Shape                       Formula
Combination of Solids
Area
Volume
Area
Volume
Area
Volume
4p r + 2pr h
2
p rl + 2 p r 
2
6l
2
- 2pr
2
l
3
- p r
2
l
4
p r
3
 + p r
2
h
3
_
2
p r
3
 +   p r
2
h
3
_
1
3
_
Area
Volume
2p r + 2prh + pr l
2
1
2
p r
3
 + p r
2
h +   p r
2
h
3
_ 1
3
_
2 1
 PLEASE KEEP IN MIND
SURFACE AREAS & VOLUMES
 But for surface area until and unless it is said that both the
surface areas are equal, one cannot equate it with the formula.
?
 When a form of solid is converted into another one, 
surface area may change but volume remains the same. 
Hence, we equate the formula of volume of the other object, 
to the value (in numbers) of the volume of the original object 
to know the value of the new parameter.
?
?
 For Volume of the combination of solid objects, simply
take the sum of the volume of all the objects involved. 
?
 Please make a note: Units for volume is written as 
(unit)
3
 and that of surface areas is (unit)
2
.
?
 For surface area of combination of the solid objects, only
look at the uppermost/the exposed portion of the objects.
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