Question

a square pyramid with a height of 9 inches has a volume of 300 cubic inches. how long is one of the sides of the base? label required

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. For a square base, if the side length of the base is \( s \), then 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 \( V = 300 \) cubic inches and \( h=9 \) inches. Substituting these values into the formula \( 300=\frac{1}{3}\times s^{2}\times9 \).

Step3: Simplify the equation

First, simplify the right - hand side of the equation. \( \frac{1}{3}\times9 = 3 \), so the equation becomes \( 300 = 3s^{2}\).

Step4: Solve for \( s^{2} \)

Divide both sides of the equation by 3: \( s^{2}=\frac{300}{3}=100 \).

Step5: Solve for \( s \)

Take the square root of both sides. Since \( s \) represents the length of a side, we take the positive square root. \( s=\sqrt{100} = 10 \) inches.

Answer:

The length of one of the sides of the base is 10 inches.