Question

pyramid a is a square pyramid with a base side length of 18 inches and a height of 9 inches. pyramid b has a volume of 3,136 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 $V=\frac{1}{3}s^{2}h$, where $s$ is the base side - length and $h$ is the height. Given $s = 18$ inches and $h=9$ inches.
$V_A=\frac{1}{3}\times18^{2}\times9$
$=\frac{1}{3}\times324\times9$
$ = 324\times3$
$=972$ cubic inches.

Step2: Find the ratio of volumes

Let $r$ be the ratio of the volume of Pyramid B to the volume of Pyramid A.
$r=\frac{V_B}{V_A}$, where $V_B = 3136$ cubic inches and $V_A=972$ cubic inches.
$r=\frac{3136}{972}\approx3.2263$.

Step3: Convert ratio to percentage

To convert the ratio to a percentage, multiply by 100.
$r_{percentage}=3.2263\times100 = 322.63\%$

Answer:

The volume of Pyramid B is $322.63\%$ bigger than the volume of Pyramid A.