Question

A resort features a square pyramid with a water slide. The length of the water slide is $90\%$ of the height of the pyramid. The base of the pyramid has side lengths of $60feet$. The volume of the pyramid is $60,000cubicfeet$. What is the length of the water slide?

Answer 1

Hint: Volume of pyramid is one-third of the volume of the rectangular prism.

Step 1: The volume $V$ of the prism is one-third the product of the area of the base and the height of the pyramid. Here, the given pyramid is the square pyramid as the base is square.

Step 2: The formula of the volume of the pyramid is given by: $V=\frac{1}{3}Bh$

Where $B$ is the area of the base & $h$ is the height of the pyramid.

Step 3: Here, $V=60000$ & the base area is square in shape.

Area of the base,
$B=l\times w$

Where $l$ is the length of the base and $w$ is the width of the base.

In the question, $l$ is 60 feet & $w$ is $60feet$

$B=60\times 60$

Let’s substitute the values in the formula,

$$\begin{gathered} V=\frac{1}{3}Bh \\ 60000=\frac{1}{3}\left(60\right)\left(60\right)\left(h\right) \end{gathered}$$

Solve the equation for $h$,

$$\begin{gathered} h=\frac{60000\times 3}{60\times 60} \\ h=50feet. \end{gathered}$$

Step 4: Let $x$ be the length of the slide

Since, The length of the slide is $90\%$ of the pyramid’s height $h$,

$$\begin{gathered} x=90\%·h \\ x=\frac{90}{100}·h \\ x=\frac{9}{10}h \end{gathered}$$

Step 5: We have already calculated the value of $h$

$$\begin{gathered} x=\frac{9}{10}\left(50\right) \\ x=45 \end{gathered}$$

Final Answer: Therefore, The length of the slide is $45feet$.