Question

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?

Answer 1

Yes. There is enough for everyone.

Step 1: Find the volume of the keg

Diameter : 13

Radius : 6.5

Height : 17

Formula for the area of a circle (base) is πr^2

Solve that using the above formula.

Base area = 132.73

Multiply that by the height.

Keg volume : 2,256.45 inches cubed

Step 2: Find the volume of the cups

Diameter : 3

Radius : 1.5

Height : 4 3/4

Formula for area of a circle (base) is πr^2

Solve that using the above formula.

Base area = 7.07

Multiply that by the height.

Cup volume : 33.58 inches cubed

Step 3: Multiply cup volume by 50

33.58 x 50 = 1,678.79

Step 4: Check how much root beer you have for everyone.

Root beer needed : 2,256.45

Root beer available : 1,678.79

Is there enough root beer?

Yes

Answer 2

Yes, there will be enough root beer for everyone to have at least one cup

Explanation:

step 1

Find the volume of the cylinder root beer keg

The volume is equal to

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

we have

`r=13/2=6.5\ in` -----> the radius is half the diameter

`h=17\ in`

substitute

`V=\pi (6.5)^(2) (17)`

`V=718.25\pi\ in^(3)`

step 2

Find the volume of the cylinder cups

The volume is equal to

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

we have

`r=3/2=1.5\ in` -----> the radius is half the diameter

`h=4(3)/(4)\ in=4.75\ in`

substitute

`V=\pi (1.5)^(2) (4.75)`

`V=10.6875\pi\ in^(3)`

step 3

Multiply 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

`10.6875\pi*(50)=534.375\pi\ in^(3)`

`534.375\pi\ in^(3)< 718.25\pi\ in^(3)`

therefore

There will be enough root beer for everyone to have at least one cup