Question

Find the volume of a right circular cone that has a height of 17 ft and a base with a circumference of 5 ft. Round your answer to the nearest tenth of a cubic foot.

Answer 1

V = 11.3 ft^3

Explanation:

The volume of a cone is given by one third of its base area multiplied by its height:

V = (1/3)*A*h

This cone have a circular base, so the base area is given by

A = pi*r^2, where r is the base radius

The length of a circumference is given by L = 2*pi*r

the base circumference is 5 ft, so we can calculate the base radius:

5 = 2*pi*r -> r = 5/(2*pi)

Using this value, we can calculate A:

A = pi*r^2 = pi * [5/(2*pi)]^2 = pi * 25/(4*pi^2) = 25/(4*pi) = 1.9894

Now, we use the formula to calculate the volume:

V = (1/3)*A*h = (1/3) * 1.9894 * 17 = 11.2735 ft^3

rounding it, we have V = 11.3 ft^3