Calculus Word Problems?

Question

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

2. A power station and a factory are on opposite sides of a river 2 km wide. A power line must be run from the power station. It costs $25.00 per meter to run the cable in the river and $20.00 per meter on land. Express the total cost as a function of x.

Answer 1

V=πr²h = 400π
h=400/r²
Cost = (.03)2πr²+(.02)2πrh
=2π(.03r² + .02(400/r))
=2π(.03r² +8/r)


x = distance on land
2000=distance in river
Cost = 25x + 20(2000-x)
=5x+40000

Answer 2

V = pir^2h = 400 pi
h= 400 /r^2
Cost = (.03)2pir^2 + (.02) 2pir
Cost = .06pir^2 + 16pi/r

x = meters on land
Total cost = 20x + 50,000