Question

Find the volume of a right circular cone that has a height of 9.1 cm and a base with a circumference of 13.3 cm. Round your answer to the nearest tenth of a cubic
centimeter.

Answer 1

Answer:

Volume = 42.8 cubic centimeters

Step-by-step explanation:

The volume of right circular cone is:

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

Where

r is the radius

h is the height

We are given height of 9.1 cm

h = 9.1

We aren't given radius explicitly, we are given circumference of 13.3, so we need to figure out radius from that. Lets do this:

$C=2\pi r\\13.3=2\pi r\\r=\frac{13.3}{2\pi}\\r=2.12$

So,

r = 2.12

Now, substituting in cone formula, we get the volume to be:

$V=\frac{1}{3}\pi r^2 h\\V=\frac{1}{3}\pi (2.12)^2 (9.1)\\V=42.83$

Rounded to nearest 10th is 1 decimal place, so

Volume = 42.8 cubic centimeters