Question

Find the volume of a right circular cone that has a height of 12.5 cm and a base with a circumference of 5.8 cm. Round your answer to the nearest tenth of a cubic centimeter.

Answer 1

11.2 is the answer.

Explanation:

Answer 2

`V = 11.2 cm^3`

Explanation:

Given

Shape: Right Circular cone

Height, h = 12.5 cm

Base circumference, C = 5.8cm

Required:

Calculate Volume

The volume of a cone is calculated as thus;

Volume,
`V = (1)/(3)\pi r^2h`

Where V, r and h represent the volume, the radius and the height of the cone respectively

But first we need to calculate the radius of the cone.

Using formula of circumference.

`C = 2\pi r`

We have C to be 5.8cm

By substituting this value;

`5.8 = 2\pi r`

Divide through by
`2\pi`

`(5.8)/(2\pi) = (2\pi r)/(2\pi)`

`r = (5.8)/(2\pi)`

`r = (2.9)/(\pi)`

Now, we can calculate the volume of the cone

By substituting
`r = (2.9)/(\pi)` and h = 12.5 cm;

`V = (1)/(3)\pi r^2h` becomes

`V = (1)/(3)\pi * ((2.9)/(\pi))^2 * 12.5`

`V = (1)/(3)\pi * (8.41)/(\pi^2) * 12.5`

`V = (1)/(3) * (8.41)/(\pi) * 12.5`

Take
`\pi` as 3.14

`V = (1)/(3) * (8.41)/(3.14) * 12.5`

`V = 11.15976`

`V = 11.2 cm^3` ---- Approximated

Hence, the volume of the cone is;
`V = 11.2 cm^3`