Algebra II Word Problem

[just.alliegator]

A cylindrical can has a volume of 400picm^3. The material for the top and bottom surfaces costs 2 cents per square centimeter. The vertical surface costs 1 cent per square centimeter. Express the costs of materials used to make the can as a function of the radius r.

I have to investigate this situation, and to do so I need an equation. I have looked around and found what help I could from other posts, but none shared my exact measurements so I wanted to see if someone could check my work. Thank you in advance!

Area of a circle: pir^2
Cost of the lid and bottom: 0.02
Therefore: 2pir^2(0.02)

Area of the side of a cylinder: 2pirh
Cost of the side: 0.01
Therefore: 2pirh(0.02)

Finding h
V = pir^2h
400pi = pir^2h
h = 400pi/pir^2
h = 400/r^2

Final equation
f(r) = 2pir^2(0.02) + 2pir(400/r^2)(0.01)

 

[mmm4444bot]

V = pi*r^2*h
400*pi = pi*r^2*h
h = 400*pi/(pi*r^2)
h = 400/r^2

Final equation
f(r) = 2pir^2(0.02) + 2pir(400/r^2)(0.01)

I agree with your function f, but please read my comments.

The added grouping symbols (shown in red above) are very important when typing rational expressions; without them, the Order of Operations would place r^2 in the numerator.

Also, you simplified your result for h, by canceling the common factors of pi. You could simplify your expression for f(r), too, by canceling the common factors of r and multiplying the constants.

Lastly, did you notice the multiplication operators (*) that I inserted above. It's a bit awkward to read things like:

400picm^3
2pir^2
2pirh(0.02)

Or, you could use word spaces.

400 pi cm^3
2 pi r^2
2 pi r h(0.02)

Otherwise, good job! :cool: