Question

question 16 a cone - shaped pile of sawdust has a base diameter of 28 feet, and is 10 feet tall. find the volume of the pile. ft.³ round your answer to the nearest tenth if necessary. question help: message instructor submit question

Explanation:

Step1: Find the radius of the base

The diameter is 28 feet, so the radius \( r = \frac{28}{2}=14 \) feet.

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 \( r \) is the radius and \( h \) is the height. Here, \( r = 14 \) feet and \( h = 10 \) feet.

Step3: Substitute the values into the formula

\( V=\frac{1}{3}\times\pi\times(14)^{2}\times 10 \)
First, calculate \( 14^{2}=196 \). Then, \( \frac{1}{3}\times\pi\times196\times 10=\frac{1960\pi}{3}\approx\frac{1960\times 3.14159}{3} \)
\( \frac{1960\times 3.14159}{3}\approx\frac{6157.52}{3}\approx 2052.5 \)

Answer:

\( 2052.5 \)