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25 vote

The radius and height of a right circular cone are in the ratio 3 : 4. If its volume is 96 π cm3, what is its slant height?

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The radius and height of a right circular cone are in the ratio 3 : 4. If its volume is 96 π cm3, what is its slant height?
1). 9 cm
2). 8 cm
3). 10 cm
4). 12 cm


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1 answers

38 vote
Answered by on | Votes 38 |

Let r = radius of base and h = height

Volume of cone = (1/3) × πr2h

Given,

⇒ (r/h) = 3/4

⇒ r = 3h/4

⇒ 96π = (1/3) × (π) × (3h/4) × (3h/4) × h

⇒ 4608 = 9h3

⇒ h = 8

Radius of base = 6 cm

∴ Slant height = $(\sqrt {{6^2} + {8^2}} = 10cm)$
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