Question

Finding volume of a sphere using cylindrical beaker and water.

i. Take a ball and a beaker of the same radius. 

ii. Cut a strip of paper of length equal to the diameter of the beaker. 

iii. Draw two lines on the strip dividing it into three equal parts. 

iv. Stick this strip on the beaker straight up from the bottom. 

v. Fill the water in the beaker upto the first mark of the strip from bottom.

vi. Push the ball in the beaker so that it touches the bottom.

Observe how much water level rises. 

You will notice that the water level has risen exactly upto the total height of the strip. Try to obtain the formula for volume of sphere using the volume of the cylindrical beaker.

Answer 1

Suppose volume of beaker upto height 2r is V. 

V = πr² h 

∴ V = πr² (2r) …[∵ h = 2r] 

∴ V = 2πr³ 

But, V = volume of the ball + volume of water in the beaker 

∴ 2πr = Volume of the ball + 1/3 × 2πr³ 

∴ Volume of the ball = 2πr³ – πr³ 

= (6πr³ − 2πr³)/3

∴ Volume of the ball = 4/3πr³ 

∴ Volume of a sphere = 4/3πr³