Question

The volume of a right circular cone is 2,279.64 in cubed. If the height of the cone is 18 in, what is the diameter of the cone? (Use pi = 3.14)
A. 22 in
B. 60.5 in
C. 11 in
D. 121 in

Answer 1

ANSWER

A. 22 in

EXPLANATION

The volume of a cone is calculated using the formula:

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

It was given that: the volume is 2,279.64 in³

The height of the cylinder is also given as: h=18 in.

We substitute, the given values into the formula to get:

$2279.64= \frac{1}{3} \times (3.14) \times {r}^{2} \times 18$

$2279.64= 18.84 {r}^{2}$

${r}^{2} = \frac{2279.64}{18.84}$

${r}^{2} = 121$

We take positive square root to get;

$r = \sqrt{121}$

$r = 11in$

Therefore the diameter is 2(11) which is equal to 22 inches.