# Cylinders and Rational Equations

### Andrew, Bailey, Brandon

# Part 1

We first had to find the minimal cost of a Folgers Coffee can. Which the coffee can volume is 135 cubic inches and the cost of the top and bottom of the can is 6 cents per square inch and the sides cost 4 cents per square inch. From there we had to construct the formula for the volume of the Folgers can. (Shown Above). Next in part b. we had to make a net diagram of the cylinder and make a equation for a total cost. In part c. our goal was to plug in our value for height into our cost equation. In order to do this we had to solve the volume equation for H. Then substitute the result of that in for H in our cost equation. Next we had to simplify the Rational expression we had just created. (4th picture). We then had to plug our simplified expression into a calculator to find the radius. We came out with a radius of 2.43. Next we had to substitute the r value into the cost equation in order to find out the minimal cost of the can. Which came to be $6.67. Our last step was to find out what the height of the can was, we did this by substituting our r value into the height equation in part c. We determined the height of the can to be 7.281.

# Part 2

Our next job was to find the cost of our cylindrical object. Which was much easier because all we had to do was measure our object and substitute those values into the equation. We also had to tweak the equation a little, instead of 6 cents for top and bottom it changed to it was .6 cents. And .4 cents for the side of the object. We measured our height to be 8.25 and our radius to be 1.25 and the volume to be 40.47. With those h and r values plugged in, our total cost came out to be $31.79. Our two equations differed because the height and radius of the 2 cylinders measured were different and the amount for the sides and top were also different. Which will result in a different total cost.