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 the volume of Pyramid A

The formula for the volume of a square pyramid is \(V=\frac{1}{3}s^{2}h\), where \(s\) is the base - side length and \(h\) is the height.
For Pyramid A, \(s = 7\) inches and \(h=6\) inches.
\(V_{A}=\frac{1}{3}\times7^{2}\times6\)
\(=\frac{1}{3}\times49\times6\)
\(=49\times2\)
\(=98\space in^{3}\)

Step2: Calculate the ratio of the volumes

We want to find out how many times \(V_{B}\) is bigger than \(V_{A}\). Let \(n\) be the ratio, so \(n=\frac{V_{B}}{V_{A}}\)
Given \(V_{B} = 3136\space in^{3}\) and \(V_{A}=98\space in^{3}\)
\(n=\frac{3136}{98}\)
\(n = 32\)

Answer:

32