Question

Trey had a cylindrical can with a radius of 4 inches and a height of 12 inches that was completely full of beet juice. He poured the juice into cylindrical glasses that each had a radius of 2 inches and a height of 8 inches, filling

3
4
of each glass. If he emptied the can, how many glasses of juice did he have? Show your work.

Answer 1

`8\ glasses\ of\ juice`

Explanation:

step 1

Find the volume of the cylindrical can

The volume of the cylinder is equal to

`V=\pi r^(2)h`

we have

`r=4\ in\\ h=12\ in`

substitute the values

`V=\pi (4)^(2)(12)=192\pi\ in^(3)`

step 2

Find the volume of the cylindrical glasses

The volume of the cylinder is equal to

`V=\pi r^(2)h`

we have

`r=2\ in\\ h=8\ in`

substitute the values

`V=\pi (2)^(2)(8)=32\pi\ in^(3)`

Find the volume of 3/4 of the glass

`32\pi ((3)/(4))=24\pi\ in^(3)`

step 3

Divide the total volume of cylindrical can by the 3/4 volume of the glass

`192\pi\ in^(3)/24\pi\ in^(3)=8\ glasses\ of\ juice`