SOLUTION: You are an engineer for McDonalds and it is your job to develop a new small coffee cup. The average diameter of a car cup holder is between 10.10 cm and 12 cm. A small cup must h

Algebra ->  Volume -> SOLUTION: You are an engineer for McDonalds and it is your job to develop a new small coffee cup. The average diameter of a car cup holder is between 10.10 cm and 12 cm. A small cup must h      Log On


   

Question 1080011: You are an engineer for McDonalds and it is your job to develop a new small coffee cup. The average diameter of a car cup holder is between 10.10 cm and 12 cm. A small cup must hold 225 cm^3 of coffee. What is the height of your cup design?
πr^2h=225 cm^3
h=v/π5.5^2
h=225/π5.5^2
225/95.03 = 2.37 doesn't make sense

I also tried converting the cm^3 first and came up with 6.0822. I thought I had it correct with dividing 95.03nby 6.0822 to end up with 15.64 cm since that would give me a cup that is 6.2 inches tall, but then I realized I did it backwards... PLEASE help!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

average diameter of a car cup holder is between 10.10cm and 12cm
so, average radius of a car cup holder is between 5.5cm and 16cm
if given volume must be 225cm%5E3, than we have:

pi%2Ar%5E2%2Ah=225+cm%5E3 ...........if r=5.5cm
3.14%2A%285.5cm%29%5E2%2Ah=225cm%5E3+
3.14%2A30.25cm%5E2%2Ah=225cm%5E3+
94.985cm%5E2%2Ah=225cm%5E3+
h=225cm%5E3+%2F94.985cm%5E2
h=2.37cm
and
pi%2Ar%5E2%2Ah=225cm%5E3 ...........if r=6cm
3.14%2A%286cm%29%5E2%2Ah=225cm%5E3

3.14%2A36cm%5E2%2Ah=225cm%5E3+
113.04cm%5E2%2Ah=225cm%5E3+
h=225cm%5E3+%2F113.04cm%5E2
h=1.99cm
so, the height of your small cup design is between 1.99cm and 2.37cm