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. Then $V_A=\frac{1}{3}\times18^{2}\times9$.
$V_A=\frac{1}{3}\times324\times9 = 324\times3=972$ cubic inches.

Step2: Calculate the ratio of volumes

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

Step3: Convert ratio to percentage

To convert the ratio to a percentage, we multiply $r$ by 100. $r\times100=\frac{3136}{972}\times100=\frac{313600}{972}\approx322.63\%$.

Answer:

$322.63\%$