Question

The figure is a sphere with a cone within it. To the nearest whole number, what is the approximate volume of the shaded part of this figure? Use 3.14 for Pi. Drag the correct value to the box.
13
113
503
29
92

Answer 1

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 = $92m^3$

Answer 2

The answer is 92 
Hope this helps!!!