Question

find the height of a pyramid with a volume of 960 in³ if the base is a square with a side length of 12 in. ?in

Explanation:

Step1: Calculate the base area

The base is a square with side length \(s = 12\) in. The area of a square is \(A=s^{2}\), so \(A = 12^{2}=144\) \(in^{2}\).

Step2: Use the pyramid volume formula

The volume formula for a pyramid is \(V=\frac{1}{3}Ah\), where \(V = 960\) \(in^{3}\) and \(A = 144\) \(in^{2}\). Rearranging for \(h\), we get \(h=\frac{3V}{A}\).
Substitute \(V = 960\) and \(A = 144\) into the formula: \(h=\frac{3\times960}{144}\).
First, calculate \(3\times960 = 2880\). Then, \(\frac{2880}{144}=20\).

Answer:

\(20\)