2 Answers

Vishnu Ranganathan · Answer 1 · 2018-01-14T19:32:13+0000

Answer

92 m³

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:

$V=(4)/(3) \pi r^3$

where

is the volume of the sphere

is the radius

We can infer from our picture that r = 3 m, so let's replace the value

V=(4)/(3) (3.14) (3m)^3

V=(4)/(3) (3.14) (27m^3)

V=113.04m^3

Volume of the cone:

$V=\pi r^2(h)/(3)$

where

is the volume of the cone

is the radius

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(5m)/(3)

V=(3.14)(4m^2)(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