Answer:
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
[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 2
Find the volume of the cylinder cups
The 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 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
[tex]10.6875\pi*(50)=534.375\pi\ in^{3}[/tex]
[tex]534.375\pi\ in^{3}< 718.25\pi\ in^{3} [/tex]
therefore
There will be enough root beer for everyone to have at least one cup
Answer:
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
