Question

a stone pyramid in egypt with a square base has a height of 121 meters. the volume is 284592 cubic meters. what is the length of the pyramid? length =

Explanation:

Step1: Recall pyramid volume formula

The volume \( V \) of a square - based pyramid is given by the formula \( V=\frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height of the pyramid. Since the base is a square with side length \( s \), the area of the base \( B = s^{2}\). So the volume formula can be rewritten as \( V=\frac{1}{3}s^{2}h \).

Step2: Substitute known values

We know that \( V = 284592\) cubic meters and \( h=121\) meters. Substitute these values into the formula:
\( 284592=\frac{1}{3}\times s^{2}\times121 \)

Step3: Solve for \( s^{2} \)

First, multiply both sides of the equation by 3 to get rid of the fraction:
\( 284592\times3 = s^{2}\times121 \)
\( 853776=s^{2}\times121 \)
Then, divide both sides by 121 to solve for \( s^{2} \):
\( s^{2}=\frac{853776}{121} \)
Calculate \( \frac{853776}{121}=7056 \)

Step4: Solve for \( s \)

Take the square root of both sides to find \( s \). Since \( s \) represents the length of a side of the base (a positive quantity), we have:
\( s = \sqrt{7056}=84 \)

Answer:

The length of the side of the square base of the pyramid is 84 meters.