Use the formula for the volume of a cone to determine the volume of each paper cup.
B
Calculate the difference between the number of paper bags that are bought and the number that is needed.
A
5 packages
B
86 paper cups
Practice makes perfect
We want to determine how many packages of paper cups we should buy to sell our lemonade. Let's start by calculating the volume of lemonade that fits in each paper cup.
The formula for volume requires us to know the radius of the base of the cone, so we need to divide the diameter by 2 to get the radius of the circular base.
d/2=r ⇒ 8/2= 4Next, we can use the formula for the volume of a cone to find the volume of one paper cup. Let's substitute 4 for r and 11 for h into the formula and calculate the volume V.
We can fill each cup with 184.3 cubic centimeters of lemonade. Now, we need to convert the total amount of lemonade from gallons to cubic centimeters. We are given the conversion factor, 1 gallon equals 3785 cubic centimeters.
10 gal * 3785 cm^3/1 gal = 37 850cm^3
We can divide the total amount of lemonade by the volume of each paper cup to determine how many paper cups we need.
37 850cm^3/184.3cm^3per cup≈ 205cups
Finally, we determine how many packages we should buy. Every package contains 50 paper cups.
205cups/50cups per package=4.1packages
It is only possible to buy whole packages. Therefore, we should buy 5 packages to have enough cups for all the lemonade.
In this part, we want to determine how many cups will be left over if we sell 80 % of the lemonade. In Part A, we found that we have 37 850 cubic centimeters of lemonade. Let's multiply this amount by 0.8 to get the volume that corresponds to 80 % of the total volume.
37 850 * 0.8 = 30 280This means that we will sell 30 280 cubic centimeters of lemonade. We also found in Part A that each paper cup has a volume of 184.3 cubic centimeters. Let's divide the total volume by the volume of each paper cup to determine how many paper cups we will use.
30 280cm^3/184.3cm^3per cup≈ 164cups
Finally, we can calculate how many cups will be left over. Remember, we will buy 5 packages of paper cups that contain 50 cups each and we only use 164 cups. Let's determine the difference.
