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?

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

Step-by-step explanation:

step 1

Find the volume of the cylinder root beer keg

The volume is equal to

we have

-----> the radius is half the diameter

substitute

step 2

Find the volume of the cylinder cups

The volume is equal to

we have

-----> the radius is half the diameter

substitute

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

therefore

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

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

this is answer of 144 cubic meters

if you was gonna solve for a, a is a   < -12