Question

a cone has a height of 17 millimeters and a diameter of 14 millimeters. what is its volume? round your answer to the nearest hundredth. cubic millimeters

Explanation:

Step1: Find the radius

The diameter is 14 mm, so the radius \( r = \frac{14}{2}=7 \) mm.

Step2: Recall the volume formula for a cone

The volume \( V \) of a cone is given by \( V=\frac{1}{3}\pi r^{2}h \), where \( h = 17 \) mm (height), \( r = 7 \) mm (radius).

Step3: Substitute the values into the formula

\( V=\frac{1}{3}\times\pi\times7^{2}\times17 \)
First, calculate \( 7^{2}=49 \), then \( \frac{1}{3}\times\pi\times49\times17=\frac{833\pi}{3}\approx\frac{833\times3.1416}{3} \)
Calculate \( 833\times3.1416 = 2617.9528 \), then \( \frac{2617.9528}{3}\approx872.65 \)

Answer:

\( 872.65 \)