Question

what is the volume of the given figure? 120 ft³ 30 ft³ 60 ft³ 90 ft³

Explanation:

Step1: Calculate the base area

The base is a rectangle with length \( l = 5\) feet and width \( w = 4\) feet. The area of a rectangle is \(A = l\times w\).

$$A=5\times4 = 20\space ft^{2}$$

Step2: Use the volume formula for a pyramid

The figure is composed of two congruent pyramids with the same base. The volume of a pyramid is \(V=\frac{1}{3}Ah\). Since there are two pyramids, the total volume \(V_{total}=2\times\frac{1}{3}Ah\). Here, \(A = 20\space ft^{2}\) and \(h = 9\div2 = 4.5\) feet (because the height of each pyramid is half of the total vertical distance between the two apexes). But another way: we can also use the fact that the formula for the volume of two - pyramid structure (bipyramid) with base area \(A\) and the total height (distance between the two apexes) \(H\) is \(V=\frac{1}{3}AH\). Substituting \(A = 20\space ft^{2}\) and \(H=9\) feet.

$$V=\frac{1}{3}\times20\times9$$

$$V = 60\space ft^{3}$$

Answer:

\(60\space ft^{3}\)