An Important Question of M.L Aggarwal book of class 10 Based on Mensuration Chapter for ICSE BOARD.

The volume of a cone is the same as that of the cylinder whose height and diameter is given. Find the radius of the base of the cone if its height is also given.

This is the Question Number 06, Exercise 17.5 of M.L Aggarwal.

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# The volume of a cone is the same as that of the cylinder whose height is 9 cm and diameter 40 cm. Find the radius of the base of the cone if its height is 108 cm.

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Given height of the cylinder, h = 9 cm

Diameter of the cylinder = 40 cm

Radius of the cylinder, r = 40/2= 20 cm

Volume of the cylinder = r

^{2}h= ×20

^{2}×9= ×400×9

= 3600 cm

^{3}Height of the cone, H = 108 cm

Volume of cone = (1/3)r

^{2}h= (1/3)r

^{2}×108= 36r

^{2}Since volume of cone is equal to the volume of the cylinder, we get

36r

^{2 }= 3600r

^{2}= 3600/36r

^{2}= 100Taking square root on both sides,

r = 10 cm

Hence the radius of the cone is 10 cm.