Question

find the height of a pyramid with a volume of 128 cm³ if the base is a square with a side length of 8 cm. ?cm

Explanation:

Step1: Calculate the base area

The base is a square with side length \(a = 8\) cm. The area of a square \(A=a^{2}\), so \(A = 8^{2}=64\) \(cm^{2}\).

Step2: Use the pyramid volume formula

The volume formula for a pyramid is \(V=\frac{1}{3}Ah\), where \(V = 128\) \(cm^{3}\) and \(A = 64\) \(cm^{2}\). Rearranging for \(h\) gives \(h=\frac{3V}{A}\).
Substitute \(V = 128\) and \(A = 64\) into the formula: \(h=\frac{3\times128}{64}\).
Calculate \(\frac{3\times128}{64}=\frac{384}{64}=6\).

Answer:

\(6\)