SOLUTION: A can in the shape of a right circular cylinder is required to have a volume of 700 cubic centimeters. The top and bottom are made up of a material that costs 8¢ per square centime

Algebra ->  Volume -> SOLUTION: A can in the shape of a right circular cylinder is required to have a volume of 700 cubic centimeters. The top and bottom are made up of a material that costs 8¢ per square centime      Log On


   

Question 350885: A can in the shape of a right circular cylinder is required to have a volume of 700 cubic centimeters. The top and bottom are made up of a material that costs 8¢ per square centimeter, while the sides are made of material that costs 5¢ per square centimeter. Find a function that describes the total cost of the material as a function of the radius r of the cylinder
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
A can in the shape of a right circular cylinder is required to have a volume of 700 cubic centimeters. The top and bottom are made up of a material that costs 8¢ per square centimeter, while the sides are made of material that costs 5¢ per square centimeter. Find a function that describes the total cost of the material as a function of the radius r of the cylinder
.
Volume is
"area of bottom" times "height"
giving us (let h = height):
(3.14r^2)h = 700
Solving for h:
height = 700/(3.14r^2)
.
Area of side:
circumference * height
circumference is (pi)d or (pi)(2r) or (3.14)(2)r or 6.28r
"area of side" = 6.28r * 700/(3.14r^2) = 1400/r
.
Area of top and bottom:
(pi)r^2
= 3.14r^2
.
Cost = "top" + "bottom" + "side"
.
C(x) = .08(3.14r^2) + .08(3.14r^2) + .05(1400/r)
C(x) = 2(.08(3.14r^2)) + .05(1400/r)
C(x) = .5024r^2 + 70/r (this is what they're looking for)
where C(x) is the cost