Answer
92 m³
Explanation
First we are going to find the volumes of the sphere and cone separately; then, we'll subtract the volume of the cone from the volume of the sphere.
Volume of the sphere:
[tex]V=\frac{4}{3} \pi r^3[/tex]
where
[tex]V[/tex] is the volume of the sphere
[tex]r[/tex] is the radius
We can infer from our picture that r = 3 m, so let's replace the value
[tex]V=\frac{4}{3} (3.14) (3m)^3[/tex]
[tex]V=\frac{4}{3} (3.14) (27m^3)[/tex]
[tex]V=113.04m^3[/tex]
Volume of the cone:
[tex]V=\pi r^2\frac{h}{3}[/tex]
where
[tex]V[/tex] is the volume of the cone
[tex]r[/tex] is the radius
[tex]h[/tex] is the height
We can infer from our picture that r = 2 m and h = 5 m, so let's replace the values
[tex]V=(3.14)(2m)^2\frac{5m}{3}[/tex]
[tex]V=(3.14)(4m^2)\frac{5m}{3}[/tex]
[tex]V=20.93m^3[/tex]
Volume of the shaded area = volume of the sphere - volume of the cone
Volume of the shaded area = [tex]113.04m^3-20.93m^3=92.11m^3[/tex]
And rounded to the nearest integer:
Volume of the shaded area = [tex]92m^3[/tex]
