If the base radius and the height of a right circular cone are increased by 10%, then the percentage increase in the volume is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 33.1%.
Formula used:
Volume of cone = 1/3πr2h
where r and h are the radius and height of the cone
Let the radius and height of the cone be 10x
Volume = 1/3π(10x)2 × 10x = 1/3π × 1000x3
Radius and height after 10% increment = 11x
Volume after radius and height increment = 1/3π(11x)2 × 11x = 1/3π × 1331x3
Required increase in volume (in %) = [(1/3π × 1331x3 - 1/3π × 1000x3)/(1/3π × 1000x3)] × 100
⇒ (331/1000) × 100 = 33.1%