Question

Find the volume of the composite solid.
24 ft
12 ft
11 ft
18 ft

Answer 1

V = 3312 ft^3

Explanation:

This figure is formed from a rectangular prism and a square-based pyramid

Given:

h (prism) = 11 ft

a (prism's base) = a (pyramid's base) = 12 × 18 = 216 ft^2

h (pyramid) = 24 - 11 = 13 ft

First, we can find the volume of the prism:

`v(prism) = a(base) * h`

`v(prism) =216* 11 = 2376 \: {ft}^(3)`

Now, let's find the volume of the pyramid:

`v(pyramid) = (1)/(3) * a(base) * h`

`v(pyramid) = (1)/(3) * 216 * 13 = 936 \: {ft}^(3)`

In order to find the total volume of the given figure, we have to add these 2 volumes together:

`v(total) = 2376 + 936 = 3312 \: {ft}^(3)`