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what is the volume of the object generated by rotating the triangle about the vertical axis?
3 in.
14 in.
axis
express your answer in terms of $\pi$.
enter your answer in the box.
volume = $\square$ in$^3$

Question

Accepted Answer

# Explanation:
## Step1: Identify the shape after rotation
When a right triangle is rotated about one of its legs (the vertical axis here), it forms a cone. The radius $ r $ of the cone is the length of the horizontal side of the triangle, and the height $ h $ is the length of the vertical side. From the diagram, $ r = 3 $ in and $ h = 14 $ in.

## Step2: 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 $.

## Step3: Substitute the values of $ r $ and $ h $ into the formula
Substitute $ r = 3 $ and $ h = 14 $ into the formula:
$$
\begin{align*}
V&=\frac{1}{3}\pi\times(3)^{2}\times14\
&=\frac{1}{3}\pi\times9\times14\
&= 3\pi\times14\
&= 42\pi
\end{align*}
$$

# Answer:
$ 42\pi $

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QUESTION IMAGE

Question

Explanation:

Step1: Identify the shape after rotation

Step2: Recall the formula for the volume of a cone

Step3: Substitute the values of \( r \) and \( h \) into the formula

Answer: