Question

find the volume of the cone given the height and radius shown. note that the figure is not to scale. round your answer to the nearest hundredth if necessary.

Explanation:

Step1: Recall the volume formula for a cone

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

Step2: Identify the values of \( r \) and \( h \)

From the figure, the radius \( r = 5 \) and the height \( h = 9 \).

Step3: Substitute the values into the formula

Substitute \( r = 5 \) and \( h = 9 \) into the formula:
\[

$$\begin{align*} V&=\frac{1}{3}\pi(5)^2(9)\\ &=\frac{1}{3}\pi(25)(9)\\ &=\frac{1}{3}\times9\times25\pi\\ & = 3\times25\pi\\ &= 75\pi \end{align*}$$

\]

Step4: Calculate the numerical value (using \( \pi\approx3.14159 \))

\[
V\approx75\times3.14159 = 235.61925
\]
Rounding to the nearest hundredth, we get \( V\approx235.62 \).

Answer:

The volume of the cone is approximately \(\boxed{235.62}\) (or if we use the exact form with \(\pi\), it is \(75\pi\approx235.62\)).