Cost of Can A is the shape of a right circular cylinder is req. to have a volume of 500 cubic cm.

Question

Cost of a Can A can in the shape of a right circular cylinder is required to have a volume of 500 cubic centimeters. The top and bottom are made of material that costs 6¢ per square centimeter, while the sides are made of material that costs 4¢ per square centimeter. Express the total cost C of the material as a function of the radius r of the cylinder. What will the cost be if the radius is 10 centimeters?

Answer 1

If r is the radius the total area of the top and bottom discs is 2πr², while the wrap-around part of the cylinder has a rectangular area of 2πrh, where h is the height of the can. The volume of the can is πr²h=500cc. Therefore, h=500/(πr²) cm.

The wrap-around part of the cylinder has an area of (2πr)(500/(πr²))=1000/r sq cm.

The cost in cents of the bottom and top discs is 6×2πr²=12πr² cents, while the cost in cents of the wrap-around part is 4000/r cents, making the total cost C(r)=12πr²+4000/r cents.

When r=10cm, C(10)=1200π+400 cents, or 12π+4 dollars. If π=3.142, then C(10)=$41.70.