CPM Homework Help : MC1 Problem 10-100

Ann and Nate's math class had a popcorn party. Each student made a container for popcorn by rolling up a piece of paper that was $11$ inches long by $14$ inches wide. Ann made a narrow tube by using the $14$ -inch side for the height. Nate made his tube shorter and wider by using the $11$ -inch side for the height.

Whose tube holds the most popcorn? How much more does it hold than the other tube?

Hint:

This is Ann's tube. You can use the same method as Nate's tube to find the volume.

This is Nate's tube. The height of the tube is $11$ inches. The circumference of the base is $14$ inches. Use this information to help you find the area of the base. Remember that, for a circle, area $= πr^{2}$ and circumference $= 2πr$ .

circumference $= 14 = 2πr$
radius $= 2.23$
area $= πr^{2} = π\left(2.23\right)^{2} = 15.60$
volume = (area of base) (height)
volume $= \left(15.60\right)\left(11\right) = 171.6$

Answer:

Nate's tube has a volume of $171.6$ cubic inches and it holds more than Ann's.
Remember to show your calculations and to figure out how much more popcorn Nate's tube holds.