Question
The radius and height of a right circular cone are in the ratio 3 : 4 . If its volume is 96`pi cm^3`. what is its slant height ?
Answer: Option C
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Let the radius and the height of the cone be `3x and 4x` respectively . Then
`1/3 xx pi xx (3x)^2 xx 4x = 96 pi`
`36x^3 = (96 xx 3)`
`hArr x^3 = ((96 xx 3)/(36))` = 8
`hArr x = 2`
`:.` Radius = 6 cm height = 8 cm .
slant height =` sqrt(6^2 + 8^2) cm = sqrt(100) cm`
= 10 cm.
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