This question was asked in 2001 cbse board exam. Question from RS Aggarwal book chapter volume and surface area of solid, page number 810, exercise 17B, problem number 10
A spherical cannon ball, 28 cm in diameter, is melted and recast into a right circular conical mould with base diameter of 35 cm. Find the height of the cone.
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Given data,
Diameter of cannon ball = 28 cm
Radius of the cannon ball = 14 cm
Let h be the height of cone.
Then
volume of conical mould = volume of spherical cannon ball
1/3π(35/2)2 h = 4/3π(14)3
∴ h = 4 × 14 × 14 × 14 × 2 × 2/35 × 35
= 896/25
= 35.84 cm.