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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.

Respuesta :

calculista

Answer:

[tex]8\ glasses\ of\ juice[/tex]

Step-by-step explanation:

step 1

Find the volume of the cylindrical can

The volume of the cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]r=4\ in\\ h=12\ in[/tex]

substitute the values

[tex]V=\pi (4)^{2}(12)=192\pi\ in^{3}[/tex]

step 2

Find the volume of the cylindrical glasses

The volume of the cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]r=2\ in\\ h=8\ in[/tex]

substitute the values

[tex]V=\pi (2)^{2}(8)=32\pi\ in^{3}[/tex]

Find the volume of 3/4 of the glass

[tex]32\pi (\frac{3}{4})=24\pi\ in^{3}[/tex]

step 3

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

[tex]192\pi\ in^{3}/24\pi\ in^{3}=8\ glasses\ of\ juice[/tex]