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Question

# If the base radius and the height of a right circular cone are increased by 20 %,then the percentage increase in volume is approximately

A

60

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B

68

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C

73

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D

78

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Solution

## The correct option is C 73 Let r be radius and h be height. Initial volume, V=13πr2h By increasing the radius, new radius r′=r+20100r=120100r=65r New height, h′=65h New volume V′=13π(r′)2h′=13π(65r)2×(65h)=13π3625r2×65h=216125(13πr2h)=216125V∴ V′=216125V∴ Increase=216125V−V=216−125125V=91125VPercentage increase=91125V×100V=3645%=73% (approx)

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