RD Sharma MCQs: Surface Area and Volume of a Sphere | Mathematics (Maths) Class 9 PDF Download

 Page 1


Q u e s t i o n : 5 6
Mark the correct alternative in each of the following:
In a sphere the number of faces is
a
1
b
2
c
3
d
4
S o l u t i o n :
A sphere has only a single face. Since there are no sides of a sphere, it has a single continuous face.
Therefore, the correct option is
a
Q u e s t i o n : 5 7
The total surface area of a hemisphere of radius r is
a
pr
2
b
2 pr
2
c
3 pr
2
d
4 pr
2
S o l u t i o n :
The curved surface area of a hemisphere of radius r is . So, the total surface area of a hemisphere will be the
sum of the curved surface area and the area of the base.
Total surface area of a hemisphere of radius r = 
Therefore, the correct option is
c
Q u e s t i o n : 5 8
The ratio of the total surface area of a sphere and a hemisphere of same radius is
a
Page 2


Q u e s t i o n : 5 6
Mark the correct alternative in each of the following:
In a sphere the number of faces is
a
1
b
2
c
3
d
4
S o l u t i o n :
A sphere has only a single face. Since there are no sides of a sphere, it has a single continuous face.
Therefore, the correct option is
a
Q u e s t i o n : 5 7
The total surface area of a hemisphere of radius r is
a
pr
2
b
2 pr
2
c
3 pr
2
d
4 pr
2
S o l u t i o n :
The curved surface area of a hemisphere of radius r is . So, the total surface area of a hemisphere will be the
sum of the curved surface area and the area of the base.
Total surface area of a hemisphere of radius r = 
Therefore, the correct option is
c
Q u e s t i o n : 5 8
The ratio of the total surface area of a sphere and a hemisphere of same radius is
a
2 : 1
b
3 : 2
c
4 : 1
d
4 : 3
S o l u t i o n :
In the given question,
The total surface area of a sphere (S
1
) = 
The total surface area of a hemisphere (S
2
) = 
So the ratio of the total surface area of a sphere and a hemisphere will be,
Therefore, the ratio of the surface areas is . So, the correct option is
d
Q u e s t i o n : 5 9
A sphere and a cube are of the same height. The ratio of their volumes is
a
3 : 4
b
21 : 11
c
4 : 3
d
11 : 21
S o l u t i o n :
In the given problem, we have a sphere and a cube of equal heights. So, let the diameter of the sphere and side of
the cube be x units.
So, volume of the sphere (V
1
) = 
Volume of the cube (V
2
) = 
So, to find the ratio of the volumes,
Page 3


Q u e s t i o n : 5 6
Mark the correct alternative in each of the following:
In a sphere the number of faces is
a
1
b
2
c
3
d
4
S o l u t i o n :
A sphere has only a single face. Since there are no sides of a sphere, it has a single continuous face.
Therefore, the correct option is
a
Q u e s t i o n : 5 7
The total surface area of a hemisphere of radius r is
a
pr
2
b
2 pr
2
c
3 pr
2
d
4 pr
2
S o l u t i o n :
The curved surface area of a hemisphere of radius r is . So, the total surface area of a hemisphere will be the
sum of the curved surface area and the area of the base.
Total surface area of a hemisphere of radius r = 
Therefore, the correct option is
c
Q u e s t i o n : 5 8
The ratio of the total surface area of a sphere and a hemisphere of same radius is
a
2 : 1
b
3 : 2
c
4 : 1
d
4 : 3
S o l u t i o n :
In the given question,
The total surface area of a sphere (S
1
) = 
The total surface area of a hemisphere (S
2
) = 
So the ratio of the total surface area of a sphere and a hemisphere will be,
Therefore, the ratio of the surface areas is . So, the correct option is
d
Q u e s t i o n : 5 9
A sphere and a cube are of the same height. The ratio of their volumes is
a
3 : 4
b
21 : 11
c
4 : 3
d
11 : 21
S o l u t i o n :
In the given problem, we have a sphere and a cube of equal heights. So, let the diameter of the sphere and side of
the cube be x units.
So, volume of the sphere (V
1
) = 
Volume of the cube (V
2
) = 
So, to find the ratio of the volumes,
Therefore, the ratio of the volumes of sphere and cube of equal heights is . So, the correct option is
d .
Q u e s t i o n : 6 0
The largest sphere is cut off from a cube of side 6 cm. The volume of the sphere will be
a
27 p
cm
3
b
36 p
cm
3
c
108 p
cm
3
d
12 p
cm
3
S o l u t i o n :
In the given problem, the largest sphere is carved out of a cube and we have to find the volume of the sphere.
Side of a cube = 6 cm
So, for the largest sphere in a cube, the diameter of the sphere will be equal to side of the cube.
Therefore, diameter of the sphere = 6 cm
Radius of the sphere = 3 cm
Now, the volume of the sphere = 
Therefore, the volume of the largest sphere inside the given cube is . So, the correct option is
b .
Q u e s t i o n : 6 1
A cylindrical rod whose height is 8 times of its radius is melted and recast into spherical balls of same radius. The
number of balls will be
a
4
Page 4


Q u e s t i o n : 5 6
Mark the correct alternative in each of the following:
In a sphere the number of faces is
a
1
b
2
c
3
d
4
S o l u t i o n :
A sphere has only a single face. Since there are no sides of a sphere, it has a single continuous face.
Therefore, the correct option is
a
Q u e s t i o n : 5 7
The total surface area of a hemisphere of radius r is
a
pr
2
b
2 pr
2
c
3 pr
2
d
4 pr
2
S o l u t i o n :
The curved surface area of a hemisphere of radius r is . So, the total surface area of a hemisphere will be the
sum of the curved surface area and the area of the base.
Total surface area of a hemisphere of radius r = 
Therefore, the correct option is
c
Q u e s t i o n : 5 8
The ratio of the total surface area of a sphere and a hemisphere of same radius is
a
2 : 1
b
3 : 2
c
4 : 1
d
4 : 3
S o l u t i o n :
In the given question,
The total surface area of a sphere (S
1
) = 
The total surface area of a hemisphere (S
2
) = 
So the ratio of the total surface area of a sphere and a hemisphere will be,
Therefore, the ratio of the surface areas is . So, the correct option is
d
Q u e s t i o n : 5 9
A sphere and a cube are of the same height. The ratio of their volumes is
a
3 : 4
b
21 : 11
c
4 : 3
d
11 : 21
S o l u t i o n :
In the given problem, we have a sphere and a cube of equal heights. So, let the diameter of the sphere and side of
the cube be x units.
So, volume of the sphere (V
1
) = 
Volume of the cube (V
2
) = 
So, to find the ratio of the volumes,
Therefore, the ratio of the volumes of sphere and cube of equal heights is . So, the correct option is
d .
Q u e s t i o n : 6 0
The largest sphere is cut off from a cube of side 6 cm. The volume of the sphere will be
a
27 p
cm
3
b
36 p
cm
3
c
108 p
cm
3
d
12 p
cm
3
S o l u t i o n :
In the given problem, the largest sphere is carved out of a cube and we have to find the volume of the sphere.
Side of a cube = 6 cm
So, for the largest sphere in a cube, the diameter of the sphere will be equal to side of the cube.
Therefore, diameter of the sphere = 6 cm
Radius of the sphere = 3 cm
Now, the volume of the sphere = 
Therefore, the volume of the largest sphere inside the given cube is . So, the correct option is
b .
Q u e s t i o n : 6 1
A cylindrical rod whose height is 8 times of its radius is melted and recast into spherical balls of same radius. The
number of balls will be
a
4
b
3
c
6
d
8
S o l u t i o n :
In the given problem, we have a cylindrical rod of the given dimensions:
Radius of the base (r
c
) = x units
Height of the cylinder (h) = 8x units
So, the volume of the cylinder (V
c
) = 
Now, this cylinder is remolded into spherical balls of same radius. So let us take the number of balls be y.
Total volume of y spheres (V
s
) = 
So, the volume of the cylinder will be equal to the total volume of y number of balls.
We get, 
Therefore, the number of balls that will be made is . So, the correct option is
c
Q u e s t i o n : 6 2
If the ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is
a
1 : 2
b
1 : 4
c
1 : 8
d
1 : 16
S o l u t i o n :
Here, we are given that the ratio of the two spheres of ratio 1:8
Page 5


Q u e s t i o n : 5 6
Mark the correct alternative in each of the following:
In a sphere the number of faces is
a
1
b
2
c
3
d
4
S o l u t i o n :
A sphere has only a single face. Since there are no sides of a sphere, it has a single continuous face.
Therefore, the correct option is
a
Q u e s t i o n : 5 7
The total surface area of a hemisphere of radius r is
a
pr
2
b
2 pr
2
c
3 pr
2
d
4 pr
2
S o l u t i o n :
The curved surface area of a hemisphere of radius r is . So, the total surface area of a hemisphere will be the
sum of the curved surface area and the area of the base.
Total surface area of a hemisphere of radius r = 
Therefore, the correct option is
c
Q u e s t i o n : 5 8
The ratio of the total surface area of a sphere and a hemisphere of same radius is
a
2 : 1
b
3 : 2
c
4 : 1
d
4 : 3
S o l u t i o n :
In the given question,
The total surface area of a sphere (S
1
) = 
The total surface area of a hemisphere (S
2
) = 
So the ratio of the total surface area of a sphere and a hemisphere will be,
Therefore, the ratio of the surface areas is . So, the correct option is
d
Q u e s t i o n : 5 9
A sphere and a cube are of the same height. The ratio of their volumes is
a
3 : 4
b
21 : 11
c
4 : 3
d
11 : 21
S o l u t i o n :
In the given problem, we have a sphere and a cube of equal heights. So, let the diameter of the sphere and side of
the cube be x units.
So, volume of the sphere (V
1
) = 
Volume of the cube (V
2
) = 
So, to find the ratio of the volumes,
Therefore, the ratio of the volumes of sphere and cube of equal heights is . So, the correct option is
d .
Q u e s t i o n : 6 0
The largest sphere is cut off from a cube of side 6 cm. The volume of the sphere will be
a
27 p
cm
3
b
36 p
cm
3
c
108 p
cm
3
d
12 p
cm
3
S o l u t i o n :
In the given problem, the largest sphere is carved out of a cube and we have to find the volume of the sphere.
Side of a cube = 6 cm
So, for the largest sphere in a cube, the diameter of the sphere will be equal to side of the cube.
Therefore, diameter of the sphere = 6 cm
Radius of the sphere = 3 cm
Now, the volume of the sphere = 
Therefore, the volume of the largest sphere inside the given cube is . So, the correct option is
b .
Q u e s t i o n : 6 1
A cylindrical rod whose height is 8 times of its radius is melted and recast into spherical balls of same radius. The
number of balls will be
a
4
b
3
c
6
d
8
S o l u t i o n :
In the given problem, we have a cylindrical rod of the given dimensions:
Radius of the base (r
c
) = x units
Height of the cylinder (h) = 8x units
So, the volume of the cylinder (V
c
) = 
Now, this cylinder is remolded into spherical balls of same radius. So let us take the number of balls be y.
Total volume of y spheres (V
s
) = 
So, the volume of the cylinder will be equal to the total volume of y number of balls.
We get, 
Therefore, the number of balls that will be made is . So, the correct option is
c
Q u e s t i o n : 6 2
If the ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is
a
1 : 2
b
1 : 4
c
1 : 8
d
1 : 16
S o l u t i o n :
Here, we are given that the ratio of the two spheres of ratio 1:8
Here, we are given that the ratio of the two spheres of ratio 1:8
Let us take,
The radius of 1
st
 sphere = r
1
The radius of 1
st
 sphere = r
2
So,
Volume of 1
st
 sphere (V
1
) = 
Volume of 2
nd
 sphere (V
2
) = 
Now, 
Now, let us find the surface areas of the two spheres
Surface area of 1
st
 sphere (S
1
) = 
Surface area of 2
nd
 sphere (S
2
) = 
So, Ratio of the surface areas,
Using
1, we get,
Therefore, the ratio of the spheres is . So, the correct option is
b
Q u e s t i o n : 6 3