Question

Find the volume of a right circular cone that has a height of 4.5 ft and a base with a circumference of 12.5 ft. Round your answer to the nearest tenth of a cubic foot.

Answer 1

Answer:

Volume of right circular cone is 18.6 cubic feet.

Solution:

We need to find volume of right circular cone

Given height of right circular cone = 4.5 feet

Given circumference of base of the cone = 12.5 feet

Formula for volume of circular cone = $\frac{\pi}{3} r^{2} h$

Where h is height and r is radius of base.

In given information we have height, but do not have radius. So first need to calculate radius of the base from given circumference of base.

Circumference of circle = $2\pi r$

Given that circumference =12.5 feet  

$12.5 = 2\pi r$

$r=\frac{12.5}{2 \pi}$

On substituting given value of height and calculated value of radius in formula of volume of cone , we get  

$\text { volume }=\frac{1}{3} \times \pi \times\left(\frac{12.5}{2 \pi}\right)^{2} \times 4.5=18.6 \text { cubic feet }$

Hence volume of right circular cone in consideration is 18.6 cubic feet.