What is the volume of a right circular cone if the circumference of the base is 125.6 ft and the height is 75 ft.?

Mathematics

1 answer:

Eddi Din [679]3 years ago

3 0

Answer:

Hence the volume of the cone is 31384.52 cubic feet

Step-by-step explanation:

We must first need to understand how the volume of a cone is calculated.

It is simply calculated by multiplying the base area of the cone by the height, and dividing the result by 3.

This is :

Volume of cone = $\frac{\pi r^2 h}{3}$

we are not given the base area of the cone. However, we are given the circumference from which we can get the radius of the base.

Circumference =

$2 \pi r=125.6ft\\r =125.6/2 \pi=19.99ft$

hence the volume of the cone is

$\frac{\pi (19.99)^2 75}{3}=31384.52ft^{3}$

Hence the volume of the cone is 31384.52 cubic feet

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