Question

a cone - shaped pile of sawdust has a base diameter of 38 feet, and is 15 feet tall. find the volume of the pile.
5670.5 × ft.³
round your answer to the nearest tenth if necessary.
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Explanation:

Step1: Find the radius of the base

The diameter is 38 feet, so the radius \( r = \frac{38}{2} = 19 \) 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 \( h \) is the height.

Step3: Substitute the values into the formula

Here, \( r = 19 \) feet and \( h = 15 \) feet. So,
\[

$$\begin{align*} V&=\frac{1}{3}\times\pi\times(19)^2\times15\\ &=\frac{1}{3}\times\pi\times361\times15\\ &=\pi\times361\times5\\ & = 1805\pi\\ &\approx1805\times3.1416\\ &\approx5669.9 \end{align*}$$

\]

Answer:

\( 5669.9 \) (or if using a more precise value of \( \pi \), it could be adjusted, but this is rounded to the nearest tenth)