Question

Which expressions represent the volume of the composite figure (the shaded figure)? Check all that apply.

(7)(12)(10) – π(32)(10)
One-third(7)(12)(10) – One-thirdπ(32)(10)
One-third(7)(12)(10) + One-thirdπ(32)(10)
280 – 30π
280 + 30π
840 – 90π

Answer 1

It’s #2 and #4

Explanation:

Edge2020

Answer 2

One-third(7)(12)(10) – One-thirdπ(3^2)(10)

280 – 30π

Explanation:

step 1

Find the volume of the cone

The volume of the cone is equal to

`V=(1)/(3)\pi r^(2)h`

we have

`r=6/2=3\ units` ---> the radius is half the diameter

`h=10\ units`

substitute

`V=(1)/(3)\pi (3)^(2)(10)`

`V=30\pi\ units^3`

step 2

Find the volume of the rectangular pyramid

The volume of the pyramid is equal to

`V=(1)/(3)Bh`

where

B is the area of the base

h is the height of the pyramid

`B=(7)(12)=84\ units^2`

`h=10\ units`

substitute

`V=(1)/(3)(84)(10)`

`V=280\ units^3`

step 3

Find the volume of the composite figure

we know that

The volume of the composite figure is equal to subtract the volume of the cone from the volume of the rectangular pyramid

so

`V=(280-30\pi)\ units^3`