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

Answer:

$8\ glasses\ of\ juice$

Step-by-step 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

$32\pi (\frac{3}{4})=24\pi\ in^{3}$

step 3

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

$192\pi\ in^{3}/24\pi\ in^{3}=8\ glasses\ of\ juice$