question 7
suppose this two - dimensional figure is rotated 360 degrees using the vertical axis shown. each small square on the grid represents 1 square inch.
what is the volume of the three - dimensional figure? round the answer to the nearest tenth.

Question

Accepted Answer

# Explanation:
## Step1: Identify the shapes formed
When the figure is rotated, it forms a cylinder and a cone.
## Step2: Calculate the volume of the cylinder
The formula for the volume of a cylinder is $V_{cylinder}=\pi r^{2}h$. The radius $r = 2$ inches (since each square is 1 inch), and the height $h = 3$ inches.
$$
\begin{align*}
V_{cylinder}&=\pi\times(2)^{2}\times3\
&=12\pi
\end{align*}
$$
## Step3: Calculate the volume of the cone
The formula for the volume of a cone is $V_{cone}=\frac{1}{3}\pi r^{2}h$. Here, $r = 2$ inches and $h = 1$ inch.
$$
\begin{align*}
V_{cone}&=\frac{1}{3}\pi\times(2)^{2}\times1\
&=\frac{4}{3}\pi
\end{align*}
$$
## Step4: Find the total volume
Add the volumes of the cylinder and the cone: $V = V_{cylinder}+V_{cone}=12\pi+\frac{4}{3}\pi=\frac{36\pi + 4\pi}{3}=\frac{40\pi}{3}$
$$
\begin{align*}
V&=\frac{40\times3.14}{3}\
&=\frac{125.6}{3}\
&\approx41.9
\end{align*}
$$

# Answer:
$41.9$

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QUESTION IMAGE

Question

Explanation:

Step1: Identify the shapes formed

Step2: Calculate the volume of the cylinder

Step3: Calculate the volume of the cone

Step4: Find the total volume

Answer: