# Linking Cans, Cylinders and Rational Equations

By: Sable Heimer, Alexyz Sanchez, Clara Lopez

Part 1:

Folgers Coffee Company wants to create a can that will hold 135 cubic inches of coffee grounds, and they also want to go green with their product. They want the can to cost no more than the sum of (6 cents per sq. inch of the top and bottom) and (4 cent per sq. in of the sides). To find the cost of the product you have to follow the equation:

Minimum Cost= 0.06[2(pi*r^2)] + 0.04(2*pi*r*h)

Volume equation: 135=pi*r^2*h

When you figure it out, you get the measurements of 5.6 inches for the height and 2.77 inches for the radius for the top and bottom of the can. You then substitute the radius and the height into the formulas:

Min. Cost= 0.06[2(pi* 2.77^2*5.6)] + 0.04(2*pi*2.7*5.6)

=0.06[2(134.99)] +0.04(95)

= 8.09+ 3.80

Min. Cost=$11.89

Volume:135=pi*r^2*h

135=pi*2.7^2*5.6

135=pi*7.67*5.6

135=135

Part 2:

For our can that we had (shown at top of poster) we got the measurements of:

Radius: 2.05 in.

Height: 6 in.

Volume: 32 oz.

Equation we used to find the minimum cost and the volume of the cylinder:

=.06[2(pi *radius^2)]+0.04(2*pi*r*h)

Our work:

Min. Cost= 0.06[2(pi*r^2)] + 0.04(2*pi*r*h)

=0.06[2(pi *2.05^2)]+0.04(2*pi*2.05*6)

=0.39+3.09

Min. Cost=$3.48

Volume=32 oz.