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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
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.
The actual question was...The volume of an oblique cone with an equal diameter and height is 18 pi cm^3. Find the height and radius (to the nearest cm)...I wasn't able to edit the question.
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