Class 9 Exam > Class 9 Notes > Mathematics (Maths) Class 9 > RD Sharma Solutions: Surface Area and Volume of a Sphere- 2
Surface Area and Volume of a Sphere- 2 RD Sharma Solutions | Mathematics (Maths) Class 9 PDF Download
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Page 1
Q u e s t i o n : 1 4
Find the volume of a sphere whose radius is:
i
2 cm
ii
3.5 cm
iii
10.5 cm
S o l u t i o n :
In the given problem, we have to find the volume of the sphere of given radii.
i Radius of the sphere = 2 cm
So, volume of the sphere =
Therefore, the volume of the sphere of radius 2 cm is
ii Radius of the sphere = 3.5 cm
Page 2
Q u e s t i o n : 1 4
Find the volume of a sphere whose radius is:
i
2 cm
ii
3.5 cm
iii
10.5 cm
S o l u t i o n :
In the given problem, we have to find the volume of the sphere of given radii.
i Radius of the sphere = 2 cm
So, volume of the sphere =
Therefore, the volume of the sphere of radius 2 cm is
ii Radius of the sphere = 3.5 cm
So, volume of the sphere =
Therefore, the volume of the sphere of radius 3.5 cm is
iii Radius of the sphere = 10.5 cm
So, volume of the sphere =
Therefore, the volume of the sphere of radius 10.5 cm is
Q u e s t i o n : 1 5
Find the volume of a sphere whose diameter is:
i
14 cm
ii
3.5 dm
iii
2.1 m
S o l u t i o n :
In the given problem, we have to find the volume of the spheres of different diameter.
i Diameter of the sphere = 14 cm
So, volume of the sphere =
So, the volume of the sphere of diameter 14 cm is .
ii Diameter of the sphere = 3.5 dm
So, volume of the sphere =
So, the volume of the sphere of diameter 3.5 dm is .
iii Diameter of the sphere = 2.1 m
Page 3
Q u e s t i o n : 1 4
Find the volume of a sphere whose radius is:
i
2 cm
ii
3.5 cm
iii
10.5 cm
S o l u t i o n :
In the given problem, we have to find the volume of the sphere of given radii.
i Radius of the sphere = 2 cm
So, volume of the sphere =
Therefore, the volume of the sphere of radius 2 cm is
ii Radius of the sphere = 3.5 cm
So, volume of the sphere =
Therefore, the volume of the sphere of radius 3.5 cm is
iii Radius of the sphere = 10.5 cm
So, volume of the sphere =
Therefore, the volume of the sphere of radius 10.5 cm is
Q u e s t i o n : 1 5
Find the volume of a sphere whose diameter is:
i
14 cm
ii
3.5 dm
iii
2.1 m
S o l u t i o n :
In the given problem, we have to find the volume of the spheres of different diameter.
i Diameter of the sphere = 14 cm
So, volume of the sphere =
So, the volume of the sphere of diameter 14 cm is .
ii Diameter of the sphere = 3.5 dm
So, volume of the sphere =
So, the volume of the sphere of diameter 3.5 dm is .
iii Diameter of the sphere = 2.1 m
So, volume of the sphere =
So, the volume of the sphere of diameter is .
Q u e s t i o n : 1 6
A hemispherical tank has inner radius of 2.8 m. Find its capacity in litres.
S o l u t i o n :
In the given problem, we have a hemispherical tank of the following dimensions:
Inner radius of the tank (r) = 2.8 m
So for the capacity of the tank, we need to find the volume of the hemispherical tank.
Volume of the tank =
Now, as we know,
So,
Therefore, the capacity of the tank is .
Q u e s t i o n : 1 7
A hemispherical bowl is made of steel 0.25 cm thick. The inside radius of the bowl is 5 cm. find the volume of steel
used in making the bowl.
S o l u t i o n :
In the given problem, we have a hemispherical bowl of the following dimensions:
Inner radius of the bowl
r = 5 cm
Thickness of the iron sheet = 0.25 cm
So, the outer radius of the tank
R = inner radius + thickness of the sheet
Now, we need to find the volume of steel used to make the bowl. For that we can use the formula for calculating the
volume of a hemispherical shell.
Volume of a hemispherical shell =
Page 4
Q u e s t i o n : 1 4
Find the volume of a sphere whose radius is:
i
2 cm
ii
3.5 cm
iii
10.5 cm
S o l u t i o n :
In the given problem, we have to find the volume of the sphere of given radii.
i Radius of the sphere = 2 cm
So, volume of the sphere =
Therefore, the volume of the sphere of radius 2 cm is
ii Radius of the sphere = 3.5 cm
So, volume of the sphere =
Therefore, the volume of the sphere of radius 3.5 cm is
iii Radius of the sphere = 10.5 cm
So, volume of the sphere =
Therefore, the volume of the sphere of radius 10.5 cm is
Q u e s t i o n : 1 5
Find the volume of a sphere whose diameter is:
i
14 cm
ii
3.5 dm
iii
2.1 m
S o l u t i o n :
In the given problem, we have to find the volume of the spheres of different diameter.
i Diameter of the sphere = 14 cm
So, volume of the sphere =
So, the volume of the sphere of diameter 14 cm is .
ii Diameter of the sphere = 3.5 dm
So, volume of the sphere =
So, the volume of the sphere of diameter 3.5 dm is .
iii Diameter of the sphere = 2.1 m
So, volume of the sphere =
So, the volume of the sphere of diameter is .
Q u e s t i o n : 1 6
A hemispherical tank has inner radius of 2.8 m. Find its capacity in litres.
S o l u t i o n :
In the given problem, we have a hemispherical tank of the following dimensions:
Inner radius of the tank (r) = 2.8 m
So for the capacity of the tank, we need to find the volume of the hemispherical tank.
Volume of the tank =
Now, as we know,
So,
Therefore, the capacity of the tank is .
Q u e s t i o n : 1 7
A hemispherical bowl is made of steel 0.25 cm thick. The inside radius of the bowl is 5 cm. find the volume of steel
used in making the bowl.
S o l u t i o n :
In the given problem, we have a hemispherical bowl of the following dimensions:
Inner radius of the bowl
r = 5 cm
Thickness of the iron sheet = 0.25 cm
So, the outer radius of the tank
R = inner radius + thickness of the sheet
Now, we need to find the volume of steel used to make the bowl. For that we can use the formula for calculating the
volume of a hemispherical shell.
Volume of a hemispherical shell =
Therefore, the volume of the iron used to make the tank is
Q u e s t i o n : 1 8
How many bullets can be made out of a cube of lead, whose edge measures 22 cm, each bullet being 2 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 = 22 cm
Diameter of the small spherical bullets
d = 2 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 : 1 9
A shopkeeper has one laddoo of radius 5 cm. With the same material, how many laddoos of radius 2.5 cm can be
made.
S o l u t i o n :
In the given problem, Let the number of smaller ladoos which can be made from a bigger ladoo be x.
Here,
The radius of the bigger ladoo (r
1
) = 5 cm
The radius of the smaller ladoo (r
2
) = 2.5 cm
So, according to the question, volume of the big ladoo is equal to the volume of x small ladoos.
Volume of the big ladoo = volume of the x small ladoos
Page 5
Q u e s t i o n : 1 4
Find the volume of a sphere whose radius is:
i
2 cm
ii
3.5 cm
iii
10.5 cm
S o l u t i o n :
In the given problem, we have to find the volume of the sphere of given radii.
i Radius of the sphere = 2 cm
So, volume of the sphere =
Therefore, the volume of the sphere of radius 2 cm is
ii Radius of the sphere = 3.5 cm
So, volume of the sphere =
Therefore, the volume of the sphere of radius 3.5 cm is
iii Radius of the sphere = 10.5 cm
So, volume of the sphere =
Therefore, the volume of the sphere of radius 10.5 cm is
Q u e s t i o n : 1 5
Find the volume of a sphere whose diameter is:
i
14 cm
ii
3.5 dm
iii
2.1 m
S o l u t i o n :
In the given problem, we have to find the volume of the spheres of different diameter.
i Diameter of the sphere = 14 cm
So, volume of the sphere =
So, the volume of the sphere of diameter 14 cm is .
ii Diameter of the sphere = 3.5 dm
So, volume of the sphere =
So, the volume of the sphere of diameter 3.5 dm is .
iii Diameter of the sphere = 2.1 m
So, volume of the sphere =
So, the volume of the sphere of diameter is .
Q u e s t i o n : 1 6
A hemispherical tank has inner radius of 2.8 m. Find its capacity in litres.
S o l u t i o n :
In the given problem, we have a hemispherical tank of the following dimensions:
Inner radius of the tank (r) = 2.8 m
So for the capacity of the tank, we need to find the volume of the hemispherical tank.
Volume of the tank =
Now, as we know,
So,
Therefore, the capacity of the tank is .
Q u e s t i o n : 1 7
A hemispherical bowl is made of steel 0.25 cm thick. The inside radius of the bowl is 5 cm. find the volume of steel
used in making the bowl.
S o l u t i o n :
In the given problem, we have a hemispherical bowl of the following dimensions:
Inner radius of the bowl
r = 5 cm
Thickness of the iron sheet = 0.25 cm
So, the outer radius of the tank
R = inner radius + thickness of the sheet
Now, we need to find the volume of steel used to make the bowl. For that we can use the formula for calculating the
volume of a hemispherical shell.
Volume of a hemispherical shell =
Therefore, the volume of the iron used to make the tank is
Q u e s t i o n : 1 8
How many bullets can be made out of a cube of lead, whose edge measures 22 cm, each bullet being 2 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 = 22 cm
Diameter of the small spherical bullets
d = 2 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 : 1 9
A shopkeeper has one laddoo of radius 5 cm. With the same material, how many laddoos of radius 2.5 cm can be
made.
S o l u t i o n :
In the given problem, Let the number of smaller ladoos which can be made from a bigger ladoo be x.
Here,
The radius of the bigger ladoo (r
1
) = 5 cm
The radius of the smaller ladoo (r
2
) = 2.5 cm
So, according to the question, volume of the big ladoo is equal to the volume of x small ladoos.
Volume of the big ladoo = volume of the x small ladoos
Therefore, can be made from one ladoo of radius 5 cm.
Q u e s t i o n : 2 0
A spherical ball of lead 3 cm in diameter is melted and recast into three spherical balls. If the diameters of two
balls be
3
2
cm and 2 cm, find the diameter of the third ball.
S o l u t i o n :
In the given problem, we have a spherical ball of lead which is remolded into 3 smaller balls.
Here, Diameter of the bigger ball (d) = 3 cm
Diameter of 1
st
small ball (d
1
) = cm
Diameter of 2
nd
small ball (d
2
) = cm
Let the diameter of the 3
rd
ball = x cm.
So now,
Volume of the bigger ball = sum of the volumes of the smaller balls
Further, solving for x, we get
Further,
Therefore, the diameter of the third ball is .
Q u e s t i o n : 2 1
A sphere of radius 5 cm is immersed in water filled in a cylinder, the level of water rises
5
3
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