Question

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 the volume of pyramid A, $V_A=\frac{1}{3}\times144\times8=384$ cubic inches.

Step2: Find the ratio of volumes

We want to find out how many times bigger the volume of pyramid B is than pyramid A. Let the ratio be $r$. We know $V_B = 3456$ cubic inches and $V_A=384$ cubic inches. The ratio $r=\frac{V_B}{V_A}=\frac{3456}{384}=9$.

Step3: Convert ratio to percentage

To convert the ratio to a percentage, we multiply the ratio by 100. So the percentage is $r\times100 = 900\%$.

Answer:

900%