Question

Your Humanities class is having a recycling project where you have to collect tin cans. If you earn $0.02 for recycling the sweet peas can from Question 5, then how much can you expect to earn for recycling a tomato can that has a 2-inch radius and a height of 5.5 inches? The recycle value is proportional to the surface area.

Answer 1

The amount for the larger can would be $0.09 if it was proportional.

First, we have to find the surface area of each can. In problem 5, we didn't find the surface area only the area around the can. We still need to add on the top and bottom of the can.

After doing that, the surface area will be 19.84 square inches.
The surface area of the larger can will be 94.2 square inches.


Just set up and solve the following proportion and you will have your answer.

0.02 / 19.84 =  x / 94.2
x = 0.09 <span />

Answer 2

First we look for the surface area of the tomato can.
 We have then:
 A = 2 * pi * r * h
 Substituting values we have:
 A = 2 * pi * 2 * 5.5
 A = 69.12
 Then, we make the following rule of three:
 12.57 in ^ 2 ------> 0.02 $
 69.12 in ^ 2 ------> k
 Clearing k we have:
 k = (69.12 / 12.57) * (0.02)
 k = 0.11 $
 Answer:
 You would expect to win:
 k = 0.11 $
 for recycling tomato cans