Question

a cone has a height of 20 inches and a radius of 7 inches. what is its volume? round your answer to the nearest hundredth. cubic inches. submit

Explanation:

Step1: Recall cone volume formula

The formula for the volume \( V \) of a cone is \( V = \frac{1}{3}\pi r^2 h \), where \( r \) is the radius and \( h \) is the height.

Step2: Substitute values

Given \( r = 7 \) inches and \( h = 20 \) inches. Substitute into the formula: \( V=\frac{1}{3}\pi(7)^2(20) \).
First, calculate \( 7^2 = 49 \). Then, \( 49\times20 = 980 \). So, \( V=\frac{1}{3}\pi\times980=\frac{980\pi}{3} \).

Step3: Compute and round

Using \( \pi\approx3.14159 \), \( \frac{980\times3.14159}{3}\approx\frac{3078.7582}{3}\approx1026.25 \) (rounded to the nearest hundredth).

Answer:

1026.25