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Volume of a Sphere


Radius of the Sphere

 

Volume of the sphere = pr3 cubic units

 

Example

If the radius of a sphere is doubled, compare the two volumes.
 

Solution

Let the radius of the original sphere be = r units.

Then radius of the new sphere = 2r units.

Let V1 = Volume of the original sphere

And V2 = Volume of the new sphere

...   
Hence,     V1:V2 = 1:8

 


 

Example

A cylindrical tub of radius 12 cm contains water upto a depth of 20 cm. A spherical iron ball is dropped into the tub. As the level of water is raised by 6.75 cm. Find the radius of the ball.
 

Solution

Let the radius of the ball be R cm.

Radius of the cylinder (r) = 12 cm

Raise in level of water in the cylinder (h) = 6.75 cm


Volume of the water displaced in the cylindrical tub on putting iron ball in it = volume of the spherical iron ball.
 

Volume of a Sphere


p R3 = p r2h

R3 = 12
´ 12 ´ 6.75

R3 = 12
´ 12 ´ 6.75 ´

R3 = 27
´ 27

R = 3
´ 3 = 9 cm

Hence, radius of the ball is 9 cm.

 

 





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