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.

Question

asked Mar 16, 2021 1.7k views

2 Answers

Vadakkumpadath · Answer 1 · 2021-03-21T17:04:00+0000

Answer:

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