Q:

There was a party with 50 students. They had a cylinder root beer keg that was 17 inches in height and 13 inches in diameter. They also had cylinder cups to drink the root beer out of, they were 3 inches in diameter and 4 3/4 inches tall. Would there be enough root beer for everyone to have at least one cup?

Accepted Solution

A:
Answer:Yes, there will be enough root beer for everyone to have at least one cupStep-by-step explanation:step 1Find the volume of the cylinder root beer kegThe volume is equal to[tex]V=\pi r^{2} h[/tex]we have[tex]r=13/2=6.5\ in[/tex] -----> the radius is half the diameter[tex]h=17\ in[/tex] substitute[tex]V=\pi (6.5)^{2} (17)[/tex][tex]V=718.25\pi\ in^{3}[/tex]step 2Find the volume of the cylinder cupsThe volume is equal to[tex]V=\pi r^{2} h[/tex]we have[tex]r=3/2=1.5\ in[/tex] -----> the radius is half the diameter[tex]h=4\frac{3}{4}\ in=4.75\ in[/tex] substitute[tex]V=\pi (1.5)^{2} (4.75)[/tex][tex]V=10.6875\pi\ in^{3}[/tex]step 3Multiply the volume of one cup by 50 (the total number of students) and then compare the result with the volume of the cylinder root beer keg so[tex]10.6875\pi*(50)=534.375\pi\ in^{3}[/tex][tex]534.375\pi\ in^{3}< 718.25\pi\ in^{3} [/tex]thereforeThere will be enough root beer for everyone to have at least one cup