You have 10 gallons of lemonade to sell. (1gal = 378 {cm}^(2)) Each customer uses 1 paper cup. The cups are sold in packages of 50. How many packages should you buy?

Question

You have 10 gallons of lemonade to sell.
`(1gal = 378 {cm}^(2))` Each customer uses 1 paper cup. The cups are sold in packages of 50. How many packages should you buy?

Answer 1

The volume of a cilinder (like the cup) is given by:

`V=\pi r^2h`

Then, each cups can hold:

`V=\pi(8)^2(11)=2211.68`

Now, since each gallon is equivalent to 3785.41 cubic cm then we have a total of 10 times 3785.41=37854.1 cubic cm of lemonade.

Therefore we need:

`(37854.1)/(2211.68)=17.11`

Hence, we need 18 cups of lemonade and we only have to buy one package.