Question

monica sells lemonade over the summer and uses conical paper cups to serve the lemonade. Each cup is 8 centimeters tall.She starts with a 10 gallon container(one gallon equivalent to 3785 cm3). part A: determine how many paper cups are needed to empty the entire 10 gallon cooler. Part B: if the conical cups are sold in packages of 50, how many packages are needed to be bought?

Answer 1

(a)205

(b)5 Packages

Explanation:

`\text{One gallon is equivalent to 3785 } cm^3`

Therefore:
`\text{10 gallon= 3785X 10 =37850 } cm^3`

Therefore, Volume of the lemonade Monica Started with is
`\text{37850 } cm^3`

The diameter of the cup =8cm

Therefore, Radius =8/2 =4cm

Height of the Cup =11cm

Volume of a Cone=
`(1)/(3)\pi r^2 h`

`\text{Volume of the Cup}=(1)/(3)\pi *4^2*11 \\=184.31cm^3`

The number of cups needed to empty the 10 gallon cooler =37850÷184.31

=205.36

`\approx 205` Cups

(b)If the Cups are sold in packages of 50

Number of Package to be bought =205 ÷ 50 =4.1

She would need to buy 5 packages.