Class 9 Maths Question Answers - Surface Area and Volume of a Sphere

 Page 1


Q u e s t i o n : 4 6
Find the surface area of a sphere of radius 14 cm.
S o l u t i o n :
In the given problem, we have to find the surface area of a sphere of a given radii.
Radius of the sphere (r) = 14 cm
So, surface area of the sphere = 
Therefore, the surface area of the given sphere of radius 14 cm is .
Q u e s t i o n : 4 7
Find the total surface area of a hemisphere of radius 10 cm.
S o l u t i o n :
In the given problem, we have to find the total surface area of a hemisphere of a given radii.
Radius of the hemisphere (r) = 10 cm
So, total surface area of the hemisphere = 
Therefore, the total surface area of the given hemisphere of radius 10 cm is .
Q u e s t i o n : 4 8
Find the radius of a sphere whose surface area is 154 cm
2
.
S o l u t i o n :
In the given problem, we have to find the radius of a sphere whose surface area is given.
Surface area of the sphere (S) = 154 cm
2
Let the radius of the sphere be r cm
Now, we know that surface area of the sphere = 
So,
Further, solving for r
Therefore, the radius of the given sphere is .
Page 2


Q u e s t i o n : 4 6
Find the surface area of a sphere of radius 14 cm.
S o l u t i o n :
In the given problem, we have to find the surface area of a sphere of a given radii.
Radius of the sphere (r) = 14 cm
So, surface area of the sphere = 
Therefore, the surface area of the given sphere of radius 14 cm is .
Q u e s t i o n : 4 7
Find the total surface area of a hemisphere of radius 10 cm.
S o l u t i o n :
In the given problem, we have to find the total surface area of a hemisphere of a given radii.
Radius of the hemisphere (r) = 10 cm
So, total surface area of the hemisphere = 
Therefore, the total surface area of the given hemisphere of radius 10 cm is .
Q u e s t i o n : 4 8
Find the radius of a sphere whose surface area is 154 cm
2
.
S o l u t i o n :
In the given problem, we have to find the radius of a sphere whose surface area is given.
Surface area of the sphere (S) = 154 cm
2
Let the radius of the sphere be r cm
Now, we know that surface area of the sphere = 
So,
Further, solving for r
Therefore, the radius of the given sphere is .
Q u e s t i o n : 4 9
The hollow sphere, in which the circus motor cyclist performs his stunts, has a diameter of 7 m. Find the area
available to the motorcyclist for riding.
S o l u t i o n :
In the given problem, the area available for the motorcyclist for riding will be equal to the surface area of the hollow
sphere. So here, we have to find the surface area of a hollow sphere of a given diameter.
Diameter of the sphere (d) = 7 m
So, surface area of the sphere = 
Therefore, the area available for the motorcyclist for riding is .
Q u e s t i o n : 5 0
Find the volume of a sphere whose surface area is 154 cm2.
S o l u t i o n :
In the given problem, we have to find the volume of a sphere whose surface area is given.
So, let us first find the radius of the given sphere.
Surface area of the sphere (S) = 154 cm
2
Let the radius of the sphere be r cm
Now, we know that surface area of the sphere = 
So,
Further, solving for r
Therefore, the radius of the given sphere is 3.5 cm.
Now, the volume of the sphere = 
Therefore, the volume of the given sphere is .
Page 3


Q u e s t i o n : 4 6
Find the surface area of a sphere of radius 14 cm.
S o l u t i o n :
In the given problem, we have to find the surface area of a sphere of a given radii.
Radius of the sphere (r) = 14 cm
So, surface area of the sphere = 
Therefore, the surface area of the given sphere of radius 14 cm is .
Q u e s t i o n : 4 7
Find the total surface area of a hemisphere of radius 10 cm.
S o l u t i o n :
In the given problem, we have to find the total surface area of a hemisphere of a given radii.
Radius of the hemisphere (r) = 10 cm
So, total surface area of the hemisphere = 
Therefore, the total surface area of the given hemisphere of radius 10 cm is .
Q u e s t i o n : 4 8
Find the radius of a sphere whose surface area is 154 cm
2
.
S o l u t i o n :
In the given problem, we have to find the radius of a sphere whose surface area is given.
Surface area of the sphere (S) = 154 cm
2
Let the radius of the sphere be r cm
Now, we know that surface area of the sphere = 
So,
Further, solving for r
Therefore, the radius of the given sphere is .
Q u e s t i o n : 4 9
The hollow sphere, in which the circus motor cyclist performs his stunts, has a diameter of 7 m. Find the area
available to the motorcyclist for riding.
S o l u t i o n :
In the given problem, the area available for the motorcyclist for riding will be equal to the surface area of the hollow
sphere. So here, we have to find the surface area of a hollow sphere of a given diameter.
Diameter of the sphere (d) = 7 m
So, surface area of the sphere = 
Therefore, the area available for the motorcyclist for riding is .
Q u e s t i o n : 5 0
Find the volume of a sphere whose surface area is 154 cm2.
S o l u t i o n :
In the given problem, we have to find the volume of a sphere whose surface area is given.
So, let us first find the radius of the given sphere.
Surface area of the sphere (S) = 154 cm
2
Let the radius of the sphere be r cm
Now, we know that surface area of the sphere = 
So,
Further, solving for r
Therefore, the radius of the given sphere is 3.5 cm.
Now, the volume of the sphere = 
Therefore, the volume of the given sphere is .
Q u e s t i o n : 5 1
How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet
being 4 cm in diameter?
S o l u t i o n :
In the given problem, we have a lead cube which is remolded into small spherical bullets.
Here, edge of the cube (s) = 44 cm
Diameter of the small spherical bullets (d) = 4 cm
Now, let us take the number of small bullets be x
So, the total volume of x spherical bullets is equal to the volume of the lead cube.
Therefore, we get,
Volume of the x bullets = volume of the cube
Therefore, small bullets can be made from the given lead cube.
Q u e s t i o n : 5 2
If a sphere of radius 2r has the same volume as that of a cone with circular base of radius r, then find the height of
the cone.
S o l u t i o n :
In the given problem, we are given a cone and a sphere which have equal volumes. The dimensions of the two are;
Radius of the cone (r
c
) = r
Radius of the sphere (r
s
) = 2r
Now, let the height of the cone = h
Here, Volume of the sphere = volume of the cone
Further, solving for h
Therefore, the height of the cone is .
Q u e s t i o n : 5 3
If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively melted into a cone of base
Page 4


Q u e s t i o n : 4 6
Find the surface area of a sphere of radius 14 cm.
S o l u t i o n :
In the given problem, we have to find the surface area of a sphere of a given radii.
Radius of the sphere (r) = 14 cm
So, surface area of the sphere = 
Therefore, the surface area of the given sphere of radius 14 cm is .
Q u e s t i o n : 4 7
Find the total surface area of a hemisphere of radius 10 cm.
S o l u t i o n :
In the given problem, we have to find the total surface area of a hemisphere of a given radii.
Radius of the hemisphere (r) = 10 cm
So, total surface area of the hemisphere = 
Therefore, the total surface area of the given hemisphere of radius 10 cm is .
Q u e s t i o n : 4 8
Find the radius of a sphere whose surface area is 154 cm
2
.
S o l u t i o n :
In the given problem, we have to find the radius of a sphere whose surface area is given.
Surface area of the sphere (S) = 154 cm
2
Let the radius of the sphere be r cm
Now, we know that surface area of the sphere = 
So,
Further, solving for r
Therefore, the radius of the given sphere is .
Q u e s t i o n : 4 9
The hollow sphere, in which the circus motor cyclist performs his stunts, has a diameter of 7 m. Find the area
available to the motorcyclist for riding.
S o l u t i o n :
In the given problem, the area available for the motorcyclist for riding will be equal to the surface area of the hollow
sphere. So here, we have to find the surface area of a hollow sphere of a given diameter.
Diameter of the sphere (d) = 7 m
So, surface area of the sphere = 
Therefore, the area available for the motorcyclist for riding is .
Q u e s t i o n : 5 0
Find the volume of a sphere whose surface area is 154 cm2.
S o l u t i o n :
In the given problem, we have to find the volume of a sphere whose surface area is given.
So, let us first find the radius of the given sphere.
Surface area of the sphere (S) = 154 cm
2
Let the radius of the sphere be r cm
Now, we know that surface area of the sphere = 
So,
Further, solving for r
Therefore, the radius of the given sphere is 3.5 cm.
Now, the volume of the sphere = 
Therefore, the volume of the given sphere is .
Q u e s t i o n : 5 1
How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet
being 4 cm in diameter?
S o l u t i o n :
In the given problem, we have a lead cube which is remolded into small spherical bullets.
Here, edge of the cube (s) = 44 cm
Diameter of the small spherical bullets (d) = 4 cm
Now, let us take the number of small bullets be x
So, the total volume of x spherical bullets is equal to the volume of the lead cube.
Therefore, we get,
Volume of the x bullets = volume of the cube
Therefore, small bullets can be made from the given lead cube.
Q u e s t i o n : 5 2
If a sphere of radius 2r has the same volume as that of a cone with circular base of radius r, then find the height of
the cone.
S o l u t i o n :
In the given problem, we are given a cone and a sphere which have equal volumes. The dimensions of the two are;
Radius of the cone (r
c
) = r
Radius of the sphere (r
s
) = 2r
Now, let the height of the cone = h
Here, Volume of the sphere = volume of the cone
Further, solving for h
Therefore, the height of the cone is .
Q u e s t i o n : 5 3
If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively melted into a cone of base
diameter 8 cm, then find the height of the cone.
S o l u t i o n :
In the given problem, we have a hollow sphere of given dimensions;
Internal diameter of the sphere (d) = 4 cm
External diameter of the sphere (D) = 8 cm
Now, the given sphere is molded into a cone,
Diameter of the base of cone (d
c
) = 8 cm
Now, the volume of hollow sphere is equal to the volume of the cone.
So, let the height of cone = h cm
Therefore, we get
Volume of cone = the volume of hollow sphere
Further, solving for h,
So, height of the cone is 
Q u e s t i o n : 5 4
The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm.
Find the height of the cone.
S o l u t i o n :
In the given problem, we are given a sphere and a cone of the following dimensions:
Radius of the sphere (r
s
) = 5 cm
So, surface area of the sphere = 
Also, radius of the cone base (r
c
) = 4 cm
So, curved surface area of the cone = 
Now, it is given that the surface area of the sphere is 5 times the curved surface are of the cone. So, we get
Page 5


Q u e s t i o n : 4 6
Find the surface area of a sphere of radius 14 cm.
S o l u t i o n :
In the given problem, we have to find the surface area of a sphere of a given radii.
Radius of the sphere (r) = 14 cm
So, surface area of the sphere = 
Therefore, the surface area of the given sphere of radius 14 cm is .
Q u e s t i o n : 4 7
Find the total surface area of a hemisphere of radius 10 cm.
S o l u t i o n :
In the given problem, we have to find the total surface area of a hemisphere of a given radii.
Radius of the hemisphere (r) = 10 cm
So, total surface area of the hemisphere = 
Therefore, the total surface area of the given hemisphere of radius 10 cm is .
Q u e s t i o n : 4 8
Find the radius of a sphere whose surface area is 154 cm
2
.
S o l u t i o n :
In the given problem, we have to find the radius of a sphere whose surface area is given.
Surface area of the sphere (S) = 154 cm
2
Let the radius of the sphere be r cm
Now, we know that surface area of the sphere = 
So,
Further, solving for r
Therefore, the radius of the given sphere is .
Q u e s t i o n : 4 9
The hollow sphere, in which the circus motor cyclist performs his stunts, has a diameter of 7 m. Find the area
available to the motorcyclist for riding.
S o l u t i o n :
In the given problem, the area available for the motorcyclist for riding will be equal to the surface area of the hollow
sphere. So here, we have to find the surface area of a hollow sphere of a given diameter.
Diameter of the sphere (d) = 7 m
So, surface area of the sphere = 
Therefore, the area available for the motorcyclist for riding is .
Q u e s t i o n : 5 0
Find the volume of a sphere whose surface area is 154 cm2.
S o l u t i o n :
In the given problem, we have to find the volume of a sphere whose surface area is given.
So, let us first find the radius of the given sphere.
Surface area of the sphere (S) = 154 cm
2
Let the radius of the sphere be r cm
Now, we know that surface area of the sphere = 
So,
Further, solving for r
Therefore, the radius of the given sphere is 3.5 cm.
Now, the volume of the sphere = 
Therefore, the volume of the given sphere is .
Q u e s t i o n : 5 1
How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet
being 4 cm in diameter?
S o l u t i o n :
In the given problem, we have a lead cube which is remolded into small spherical bullets.
Here, edge of the cube (s) = 44 cm
Diameter of the small spherical bullets (d) = 4 cm
Now, let us take the number of small bullets be x
So, the total volume of x spherical bullets is equal to the volume of the lead cube.
Therefore, we get,
Volume of the x bullets = volume of the cube
Therefore, small bullets can be made from the given lead cube.
Q u e s t i o n : 5 2
If a sphere of radius 2r has the same volume as that of a cone with circular base of radius r, then find the height of
the cone.
S o l u t i o n :
In the given problem, we are given a cone and a sphere which have equal volumes. The dimensions of the two are;
Radius of the cone (r
c
) = r
Radius of the sphere (r
s
) = 2r
Now, let the height of the cone = h
Here, Volume of the sphere = volume of the cone
Further, solving for h
Therefore, the height of the cone is .
Q u e s t i o n : 5 3
If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively melted into a cone of base
diameter 8 cm, then find the height of the cone.
S o l u t i o n :
In the given problem, we have a hollow sphere of given dimensions;
Internal diameter of the sphere (d) = 4 cm
External diameter of the sphere (D) = 8 cm
Now, the given sphere is molded into a cone,
Diameter of the base of cone (d
c
) = 8 cm
Now, the volume of hollow sphere is equal to the volume of the cone.
So, let the height of cone = h cm
Therefore, we get
Volume of cone = the volume of hollow sphere
Further, solving for h,
So, height of the cone is 
Q u e s t i o n : 5 4
The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm.
Find the height of the cone.
S o l u t i o n :
In the given problem, we are given a sphere and a cone of the following dimensions:
Radius of the sphere (r
s
) = 5 cm
So, surface area of the sphere = 
Also, radius of the cone base (r
c
) = 4 cm
So, curved surface area of the cone = 
Now, it is given that the surface area of the sphere is 5 times the curved surface are of the cone. So, we get
Now, slant height (l) of a cone is given by the formula:
So, let us take the height of the cone as h,
We get,
Squaring both sides,
Further, solving for h
Therefore, height of the cone is .
Q u e s t i o n : 5 5
If a sphere is inscribed in a cube, find the ratio of the volume of cube to the volume of the sphere.
S o l u t i o n :
In the given problem, we are given a sphere inscribed in a cube. So, here we need to find the ratio between the
volume of a cube and volume of sphere. This means that the diameter of the sphere will be equal to the side of the
cube. Let us take the diameter as d.
Here,
Volume of a cube (V
1
) = 
Volume of a sphere (V
2
) = 
Now, the ratio of the volume of sphere to the volume of the cube = 
So, the ratio of the volume of cube to the volume of the sphere is .