find the volume of each of the following figures. complete parts (a) through (e) below.
a. right circular cone with hemisphere
the volume is
(type an exact ans
use integers or
fractions for any nu
ression.)

Question

Accepted Answer

# Explanation:
## Step1: Calculate the volume of the cone
The formula for the volume of a cone is $V_{cone}=\frac{1}{3}\pi r^{2}h$. Given $r = 5\space cm$ and $h=13\space cm$, we substitute these values into the formula:
$$
\begin{align*}
V_{cone}&=\frac{1}{3}\pi\times(5)^{2}\times13\
&=\frac{1}{3}\pi\times25\times 13\
&=\frac{325\pi}{3}\space cm^{3}
\end{align*}
$$
## Step2: Calculate the volume of the hemisphere
The formula for the volume of a hemisphere is $V_{hemisphere}=\frac{2}{3}\pi r^{3}$. Given $r = 5\space cm$, we substitute this value into the formula:
$$
\begin{align*}
V_{hemisphere}&=\frac{2}{3}\pi\times(5)^{3}\
&=\frac{2}{3}\pi\times125\
&=\frac{250\pi}{3}\space cm^{3}
\end{align*}
$$
## Step3: Calculate the total volume
The total volume $V = V_{cone}+V_{hemisphere}$
$$
\begin{align*}
V&=\frac{325\pi}{3}+\frac{250\pi}{3}\
&=\frac{325\pi + 250\pi}{3}\
&=\frac{575\pi}{3}\space cm^{3}
\end{align*}
$$

# Answer:
$\frac{575\pi}{3}\space cm^{3}$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the volume of the cone

Step2: Calculate the volume of the hemisphere

Step3: Calculate the total volume

Answer: