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:
\(V=\frac{4}{3} \pi r^3\)
where
\(V\) is the volume of the sphere
\(r\) is the radius
We can infer from our picture that r = 3 m, so let's replace the value
\(V=\frac{4}{3} (3.14) (3m)^3\)
\(V=\frac{4}{3} (3.14) (27m^3)\)
\(V=113.04m^3\)
Volume of the cone:
\(V=\pi r^2\frac{h}{3}\)
where
\(V\) is the volume of the cone
\(r\) is the radius
\(h\) is the height
We can infer from our picture that r = 2 m and h = 5 m, so let's replace the values
\(V=(3.14)(2m)^2\frac{5m}{3}\)
\(V=(3.14)(4m^2)\frac{5m}{3}\)
\(V=20.93m^3\)
Volume of the shaded area = volume of the sphere - volume of the cone
Volume of the shaded area = \(113.04m^3-20.93m^3=92.11m^3\)
And rounded to the nearest integer:
Volume of the shaded area = \(92m^3\)
