kates chocolate wonders makes handmade chocolate bars. in the last step of the process, melted chocolate is poured from a full hemispherical bowl into chocolate-bar molds shaped like rectangular prisms. the dimensions of the bowl and one chocolate-bar mold are shown below. how many whole chocolate bars can be made from the melted chocolate in the bowl? chocolate bars

Question

Accepted Answer

# Explanation:
## Step1: Calculate the volume of the hemispherical bowl
The volume formula for a hemisphere is $V_{hemisphere}=\frac{2}{3}\pi r^{3}$. Given $r = 7$ in.
$$
\begin{align*}
V_{hemisphere}&=\frac{2}{3}\times\pi\times(7)^{3}\
&=\frac{2}{3}\times\pi\times343\
&=\frac{686\pi}{3}\text{ in}^3\
&\approx\frac{686\times3.14}{3}\
&=\frac{2154.04}{3}\
& = 718.013\text{ in}^3
\end{align*}
$$
## Step2: Calculate the volume of the rectangular - prism - shaped mold
The volume formula for a rectangular prism is $V = l\times w\times h$. Given $l = 5.25$ in, $w = 3$ in, $h=0.35$ in
$$
\begin{align*}
V_{mold}&=5.25\times3\times0.35\
&=15.75\times0.35\
&= 5.5125\text{ in}^3
\end{align*}
$$
## Step3: Find the number of chocolate bars
Divide the volume of the hemisphere by the volume of the mold. $n=\frac{V_{hemisphere}}{V_{mold}}$
$$
n=\frac{718.013}{5.5125}\approx130.25
$$

# Answer:
$130$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the volume of the hemispherical bowl

Step2: Calculate the volume of the rectangular - prism - shaped mold

Step3: Find the number of chocolate bars

Answer: