Question

find the volume of the right cone below. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Recall the formula for the volume of a cone

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

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

From the diagram, the radius \( r = 7 \) and the height \( h=21 \).

Step3: Substitute the values into the formula

Substitute \( r = 7 \) and \( h = 21 \) into the formula \( V=\frac{1}{3}\pi r^{2}h \):
\[

$$\begin{align*} V&=\frac{1}{3}\times\pi\times(7)^{2}\times21\\ &=\frac{1}{3}\times\pi\times49\times21\\ &=\pi\times49\times7\\ & = 343\pi \end{align*}$$

\]

Step4: Calculate the numerical value

Using \( \pi\approx3.14159 \), we have \( V\approx343\times3.14159\approx1077.6 \)

Answer:

\( 1077.6 \) (If we use a more precise value of \( \pi \), the result may vary slightly, but rounded to the nearest tenth, it is \( 1077.6 \))