Question

question 1 (essay worth 10 points) pyramid a is a square pyramid with a base side length of 12 inches and a height of 8 inches. pyramid b has a volume of 3,456 cubic inches. how many times bigger is the volume of pyramid b than pyramid a? give your answer as a percentage. provide an explanation and proof for your answer to receive full credit.

Explanation:

Step1: Calculate volume of Pyramid A

The volume formula for a square - pyramid is $V=\frac{1}{3}Bh$, where $B$ is the base area and $h$ is the height. The base of Pyramid A is a square with side length $s = 12$ inches, so the base area $B=s^{2}=12^{2}=144$ square inches. The height $h = 8$ inches. Then $V_A=\frac{1}{3}\times144\times8=384$ cubic inches.

Step2: Find ratio of volumes

We want to find out how many times the volume of Pyramid B is larger than Pyramid A. Let the volume of Pyramid B be $V_B = 3456$ cubic inches. The ratio $r=\frac{V_B}{V_A}$. Substitute $V_A = 384$ and $V_B=3456$ into the formula: $r=\frac{3456}{384}=9$.

Answer:

9