Question

volume of a cone
the volume of a cone with radius ( r ) and height ( h ) is given by the formula ( v = \frac{1}{3}pi r^2 h ).
a cone - shaped pile of sawdust has a base diameter of 24 feet, and is 7 feet tall.
find the volume of the sawdust pile.
( square ) ( \text{ft}^3 )
round your answer to the nearest hundredth if necessary. use 3.14 or the ( pi ) button on your calculator.

Explanation:

Step1: Find the radius

The diameter is 24 feet, so the radius \( r=\frac{24}{2} = 12 \) feet.

Step2: Substitute into the volume formula

The volume formula for a cone is \( V=\frac{1}{3}\pi r^{2}h \). We know \( r = 12 \), \( h=7 \), and we can use \( \pi = 3.14 \). Substitute these values:
\( V=\frac{1}{3}\times3.14\times12^{2}\times7 \)
First, calculate \( 12^{2}=144 \). Then:
\( V=\frac{1}{3}\times3.14\times144\times7 \)
\( \frac{1}{3}\times144 = 48 \), so:
\( V = 3.14\times48\times7 \)
\( 3.14\times48=150.72 \), then \( 150.72\times7 = 1055.04 \)

Answer:

\( 1055.04 \)