a square pyramid with a height of 9 inches has a volume of 300 cubic inches. how long is one of the sides of…

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.