Question

Find the volume of the figure.

A) 1224 m3
B) 2160 m3
C) 6480 m3
D) 2851 m3

Answer 1

`$(B) 2160 m^3`

Explanation:

Volume of a Pyramid
`=(1)/(3)$ X Base Area X Height`

In the right triangle at the base, Hypotenuse=30m and Height =24m.

We use Pythagorean Theorem to determine the base of the triangle.

`30^2=24^2+b^2\\b^2=30^2-24^2\\b^2=324\\b^2=18^2\\$Base of the right triangle =18m`

Therefore:

Area of the Right Triangle =0.5 X 18 X 24 =216 square meters

• Base Area of the Pyramid=216 square meters
• Height of the Pyramid=30m

Therefore, the volume of the figure

`=(1)/(3)$ X 216 X 30\\\\=2160m^3`

The correct option is B.