find the volume of the cone given the height and radius shown. note that the figure is not to scale. round…

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)).