find the volume of the solid generated when the right triangle below is rotated about side (overline{ik}). round your answer to the nearest tenth if necessary.

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for the volume of a cone
The formula for the volume of a cone is $ V=\frac{1}{3}\pi r^{2}h$. When the right - triangle is rotated about side $IK$, side $IJ$ becomes the radius $r = 7$ and side $IK$ becomes the height $h = 8$ of the resulting cone.
## Step2: Substitute the values into the formula
Substitute $r = 7$ and $h = 8$ into the formula $V=\frac{1}{3}\pi r^{2}h$.
$$
\begin{align*}
V&=\frac{1}{3}\times\pi\times7^{2}\times8\
&=\frac{1}{3}\times\pi\times49\times8\
&=\frac{392\pi}{3}\
&\approx\frac{392\times3.14}{3}\
&=\frac{1230.88}{3}\
&\approx410.3
\end{align*}
$$

# Answer:
$410.3$ units³

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for the volume of a cone

Step2: Substitute the values into the formula

Answer: