Question

An oblique cone has a height equal to the diameter of the base. The volume of the cone is equal to 18π cubic units.



What is the radius of the cone?

2 units
3 units
6 units
9 units

Answer 1

we know that

The formula for the volume of the cone, is equal to

$V=\frac{1}{3} \pi r^{2}h$

in this problem

$V=18\pi\ unit^{3} \\\\ r=\frac{2x}{2} =x\ units \\ \\ h=2x\ units$

Substitute in the formula above

$18\pi=\frac{1}{3} \pi*x^{2}*2x$

$18\pi=\frac{1}{3} \pi*x^{2}*2x\\ \\ 54=2x^{3} \\ \\ x^{3} =27\\ \\ x=\sqrt[3]{27} \\ \\ x=3\ units$

therefore

the answer is

The radius of the cone is equal to $3\ units$

Answer 2

The radius of the cone with a volume of 18π cubic units is 3 units.

Cone

A cone is a three-dimensional solid geometric shape having a circular base and a pointed edge at the top called the vertex.

Given the diameter = 2x, height = 2x, hence:

Radius = diameter / 2 = 2x/2 = x

Volume of cone = (1/3)π * radius² * height

18π = (1/3)π * x² * 2x

2x³ = 54

x³ = 27

x = 3 units

The radius of the cone with a volume of 18π cubic units is 3 units.

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