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. 10 3

Explanation:

Step1: Recall the formula for the volume of 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 diagram, the radius \( r = 3 \) and the height \( h = 10 \).

Step3: Substitute the values into the formula

Substitute \( r = 3 \) and \( h = 10 \) into the formula:
\[

$$\begin{align*} V&=\frac{1}{3}\pi(3)^2(10)\\ &=\frac{1}{3}\pi(9)(10)\\ &= 3\pi(10)\\ &= 30\pi \end{align*}$$

\]

Step4: Calculate the numerical value (using \( \pi \approx 3.14159 \))

\[
V\approx30\times3.14159 = 94.2477
\]
Rounding to the nearest hundredth gives \( 94.25 \).

Answer:

The volume of the cone is approximately \( 94.25 \) (or exactly \( 30\pi \)). If we use \( \pi\approx3.14 \), the volume is \( 94.2 \), but with more precise \( \pi \), it's \( 94.25 \) when rounded to the nearest hundredth. The exact form is \( 30\pi \), and the approximate value (rounded to the nearest hundredth) is \( 94.25 \).