Question

Please help me!!! Geometry question.

Answer 1

The volume of the figure is
`((l^(3))/(3))[(\pi )/(2)-1]\ units^(3)`

Explanation:

we know that

The volume of the figure is equal to the volume of the cone minus the volume of the square pyramid

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=(l√(2))/(2)\ units` ----> the diagonal of the square base of pyramid is equal to the diameter of the cone

`h=l\ units`

substitute

`V=(1)/(3)\pi ((l√(2))/(2))^(2)(l)`

`V=(1)/(6)\pi (l)^(3)\ units^(3)`

step 2

Find the volume of the square 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

we have

`h=l\ units`

`B=l^(2)\ units^(2)`

substitute

`V=(1)/(3)l^(2)(l)`

`V=(1)/(3)l^(3)\ units^(3)`

step 3

Find the volume of the figure

`(1)/(6)\pi (l)^(3)\ units^(3)-(1)/(3)l^(3)\ units^(3)=((l^(3))/(3))[(\pi )/(2)-1]\ units^(3)`