How do I solve this question? It says... The volume of an oblique cone with equal diameter and height is 18`pi`

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llltkl | Student

Volume of a cone (including oblique cones) can be obtained by

V = 1/3 area of the base * height.

In the given example diameter of the base is x, so is the height of the cone.

Radius of the base = x/2

Area of the base = pi * r^2

= pi (x/2)^2

=pi x^2/4

Therefore, volume V = 1/3*pi x^2/4*x

=1/12 * pi*x^3

by the condition of the problem,

1/12 * pi*x^3 = 18*pi

`rArr x^3 = 18*12 = 216`

`rArr x=root(3)(216)= 6`

Therefore, the value of x, i.e. the diameter of the base (which is again, equal to the height) of the oblique cone is 6 units.