Question

The circumference of the base of the cone is 8.5π inches. What is the volume of the cone in terms of π? Round to the nearest hundredth. Enter your answer in the box.

Answer 1

Given:

Circumference of the base = 8.5π inches

Height of the cone = 15 inches

To find:

The volume of the cone.

Solution:

Circumference of the base is a circle.

Circumference = 2πr

2πr = 8.5π

Cancel the common factor π on both sides.

2r = 8.5

Divide by 2 on both sides, we get

r = 4.25

Volume of the cone = $\frac{1}{3}\pi r^2 h$

                                 $=\frac{1}{3} \times \pi \times (4.25)^2 \times 15$

                                 $= \pi \times 18.0625 \times 5$

                                 $=90.3125\pi$

                                 $=90.31\pi$

The volume of the cone is 90.31π.