Question

pyramid a is a square pyramid with a base side length of 7 inches and a height of 6 inches. pyramid b has a volume of 3,136 in³. how many times bigger is the volume of pyramid b than pyramid a?

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 is a square with side length $s = 7$ inches, so $B=s^{2}=7^{2}=49$ square inches, and $h = 6$ inches. Then $V_A=\frac{1}{3}\times49\times6=98$ $in^{3}$.

Step2: Find the ratio of volumes

We want to find how many times bigger the volume of Pyramid B is than Pyramid A. Let the volume of Pyramid B be $V_B = 3136$ $in^{3}$. The ratio $r=\frac{V_B}{V_A}=\frac{3136}{98}=32$.

Answer:

32