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

A. 22 in

Step-by-step explanation

The volume of a cone is calculated using the formula:

`Volume = (1)/(3) * \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= (1)/(3) * (3.14) * {r}^(2) * 18`

`2279.64= 18.84 {r}^(2)`

`{r}^(2) = (2279.64)/(18.84)`

`{r}^(2) = 121`

We take positive square root to get;

`r = √(121)`

`r = 11in`

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