Question

Monica sells lemonade over the summer and uses Conical paper cups to serve the lemonade. Each cup is 8 cm in diameter and 11 cm tall. She starts with a 10 gallon container (1 gallon is equivalent to 3085 cm)

Part A: Determine how many paper cups or needed to empty the entire 10 gallon cooler.


Part B: If the conical cups are solid and packages of 50. How many packages are needed to be bought?

Answer 1

a) 167 cups

b) 4 packages

Explanation:

Given:

Diameter, d = 8cm

Height, h = 11 cm

10 gallon container

Since 1 gallon = 3085cm, 10 gallons will be:

= 10 * 3085 = 30850 cm

a) Consider that the shape of the cup is a cone. To determine how many paper cups are needed to empty the entire 10 gallon cooler, let's first find the volume of the cone.

Formula for volume of a cone:

`V = (1)/(3) \pi r^2 h`

We know radius, r = d/2 = 8/2 = 4cm

Substituting figures in the formula, we have:

`V = (1)/(3) \pi 4^2*11`

V = 184.31 cm³

The number of paper cups are needed to empty the entire 10 gallon cooler would be:

`= (30850)/(184.31) = 167.38 cups`

Approximately 167 cups

b) if the cups are sold in packages of 50, the number of packages to be bought will be:

`= (167)/(50) = 3.34`

Which is approximately 4 packages