Question

the formula for the volume v of a pyramid is v = 1/3 bh, where b is the area of the base of the pyramid and h is the height of the pyramid. the pyramid shown has a length of 9 m and a width of 8 m. the height of the pyramid is 12 m. what is the volume of the pyramid? a. 136 m³ b. 256 m³ c. 288 m³ d. 324 m³

Explanation:

Step1: Calculate base - area

The base is a rectangle with length \(l = 9\)m and width \(w = 8\)m. The area of the base \(B=l\times w\), so \(B = 9\times8=72\) \(m^{2}\).

Step2: Use volume formula

The volume formula of a pyramid is \(V=\frac{1}{3}Bh\), where \(h = 12\)m. Substitute \(B = 72\) \(m^{2}\) and \(h = 12\)m into the formula: \(V=\frac{1}{3}\times72\times12\).
First, \(\frac{1}{3}\times72 = 24\), then \(24\times12=288\) \(m^{3}\).

Answer:

C. \(288\ m^{3}\)