Answer:
[tex]$(B) 2160 m^3[/tex]
Step-by-step explanation:
Volume of a Pyramid [tex]=\frac{1}{3}$ X Base Area X Height[/tex]
In the right triangle at the base, Hypotenuse=30m and Height =24m.
We use Pythagorean Theorem to determine the base of the triangle.
[tex]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[/tex]
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
[tex]=\frac{1}{3}$ X 216 X 30\\\\=2160m^3[/tex]
The correct option is B.
