question
find the volume of the solid generated when the right triangle below is rotated about side ( overline{hj} ).
round your answer to the nearest tenth if necessary.
answer
attempt 1 out of 2

Question

Accepted Answer

# Explanation:
## Step1: Determine the shape of the solid
When a right - triangle is rotated about one of its legs, the resulting solid is a cone. Here, the right - triangle is rotated about side $HJ$. The radius $r$ of the base of the cone is the length of the other leg ($r = 7$), and the height $h$ of the cone is the length of the axis of rotation ($h=5$).
## Step2: Use the formula for the volume of a cone
The formula for the volume $V$ of a cone is $V=\frac{1}{3}\pi r^{2}h$.
Substitute $r = 7$ and $h = 5$ into the formula:
$$
\begin{align*}
V&=\frac{1}{3}\pi\times(7)^{2}\times5\
&=\frac{1}{3}\pi\times49\times 5\
&=\frac{245\pi}{3}\
\end{align*}
$$
## Step3: Calculate the numerical value
$$
\begin{align*}
V&=\frac{245\pi}{3}\
&\approx\frac{245\times3.14}{3}\
&=\frac{769.3}{3}\
&\approx256.4
\end{align*}
$$

# Answer:
$256.4$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Determine the shape of the solid

Step2: Use the formula for the volume of a cone

Step3: Calculate the numerical value

Answer: