Question

the formula for the volume, v, of a pyramid is v = 1/3bh, where b is the area of the base of the pyramid and h is the pyramids height. 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, $B = 9\times8=72$m².

Step2: Use volume formula

The volume formula of a pyramid is $V=\frac{1}{3}Bh$, where $h = 12$m. Substitute $B = 72$m² and $h = 12$m into the formula: $V=\frac{1}{3}\times72\times12$.
First, $\frac{1}{3}\times72 = 24$, then $24\times12=288$m³.

Answer:

C. $288$ m³