bill and his dad built a tree house together. the tree house is shaped like a cube with a square pyramid loft on top. the dimensions of the tree house are shown below. what percent of the tree houses total volume is made up by the pyramid loft? round your answer to the nearest percent. %

Question

Accepted Answer

# Explanation:
## Step1: Calculate the volume of the pyramid
The formula for the volume of a square - pyramid is $V_{pyramid}=\frac{1}{3}s^{2}h$, where $s = 6.5$ ft (the base side length) and $h = 4$ ft (the height).
$$
\begin{align*}
V_{pyramid}&=\frac{1}{3}\times(6.5)^{2}\times4\
&=\frac{1}{3}\times42.25\times4\
&=\frac{169}{3}\text{ ft}^3\approx56.33\text{ ft}^3
\end{align*}
$$
## Step2: Calculate the volume of the cube
The formula for the volume of a cube is $V_{cube}=s^{3}$, where $s = 6.5$ ft.
$$
\begin{align*}
V_{cube}&=(6.5)^{3}\
&=6.5\times6.5\times6.5\
&=274.625\text{ ft}^3
\end{align*}
$$
## Step3: Calculate the total volume of the tree - house
$V_{total}=V_{pyramid}+V_{cube}$
$$
\begin{align*}
V_{total}&=\frac{169}{3}+274.625\
&=\frac{169 + 823.875}{3}\
&=\frac{992.875}{3}\text{ ft}^3\approx330.96\text{ ft}^3
\end{align*}
$$
## Step4: Calculate the percentage of the pyramid's volume in the total volume
The percentage $P=\frac{V_{pyramid}}{V_{total}}\times100\%$
$$
\begin{align*}
P&=\frac{\frac{169}{3}}{\frac{992.875}{3}}\times 100\%\
&=\frac{169}{992.875}\times100\%\
&\approx17\%
\end{align*}
$$

# Answer:
$17\%$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the volume of the pyramid

Step2: Calculate the volume of the cube

Step3: Calculate the total volume of the tree - house

Step4: Calculate the percentage of the pyramid's volume in the total volume

Answer: