Question

given this square pyramid with height = 50 m and volume = 15,000 m³, find the missing side length of the base of the pyramid:

Explanation:

Step1: Recall the volume formula for a square pyramid

The volume \( V \) of a square 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 becomes \( V=\frac{1}{3}s^{2}h \).

Step2: Substitute the given values into the formula

We know that \( V = 15000\space m^{3} \) and \( h = 50\space m \). Substituting these values into the formula \( 15000=\frac{1}{3}\times s^{2}\times50 \).

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

First, multiply both sides of the equation by 3 to get rid of the fraction: \( 15000\times3 = s^{2}\times50 \). Calculating the left side, \( 45000 = 50s^{2} \). Then, divide both sides by 50: \( s^{2}=\frac{45000}{50}=900 \).

Step4: Solve for \( s \)

Take the square root of both sides. Since \( s \) represents a length, we take the positive square root: \( s=\sqrt{900} = 30 \).

Answer:

\( 30 \)