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Question

The volume of a right circular cone is 4710 cu.cm. if the radius and height of the cone are in the ratio 3:4, find its slant height, when π=314.

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Solution

Given that
the volume of right circular
cone=4710 c.m3
and
radius:height=3:4
let radius=r
height=h
let the ratio=x
then
h=4x
r=3x
now,A.T.Q,
Volume=13πr2h
4710=13×3.14×(3x)2×4x
4710×3=36x3×3.14
x3=125
x=5
now,
radius=3x=3×5=15cm.
height=4x=4×5=20cm.
slant height(l)=h2+r2
=202+152
400+225
=625
=25c.m.
then,
slant height(l)=25 c.m.
Hence, this is the answer.

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