Question

Suppose you work for a company that manufactures cylindrical cans. Which will cost more to​ manufacture, a can with a radius of 4 inches and a height of 5 ​inches, or a can with a radius of 5 inches and a height of ​4 inches? Assume that the cost of material for the tops and bottoms is per $1.40 square inch and the cost of material for curved surfaces is $0.90 per square inch.

Answer 1

The cylinder with radius of 5 inches and height of 4 inches costs more to manufacture.

Explanation:

First Can:

Top and Bottom Surface Area = 2(pi(4)^2) = 2(16pi) = 32 pi = 100.53 square inches

Cost for top and bottom surface area = 1.40 * 100.53 = $140.74

Curved Surface Area = 2pi*r*h = 2*pi*4*5 = 40 pi = 125.66 square inches

Cost for Curved Surface Area = 125.66 * 0.90 = $113.10

Total Cost = $140.74 + $113.10 = $253.84

Second Can

Top and Bottom Surface Area = 2(pi(5)^2) = 2(25pi) = 50 pi = 157.08 square inches

Cost for top and bottom surface area = 1.40 * 157.08 = $219.91

Curved Surface Area = 2pi*r*h = 2*pi*5*4 = 40 pi = 125.66 square inches

Cost for Curved Surface Area = 125.66 * 0.90 = $113.10

Total Cost = $219.91 + $113.10 = $333.01

So, the cylinder with radius of 5 inches and height of 4 inches costs more to manufacture.

Answer 2

the can with the 5-inch radius will cost more

Explanation:

The cost will be given by the formula ...

cost = 1.40 × (top & bottom area) + 0.90 × (lateral area)

In terms of radius and height the areas are ...

top & bottom area = 2πr²

lateral area = 2πrh

So, the total cost of a can with radius r and height h is ...

c(r, h) = 1.40·2πr² +0.90·2πrh

Filling in the given values and doing the arithmetic, we find the costs to be ...

c(4, 5) = $253.84

c(5, 4) = $333.01

The cost of the can with the 5-inch radius is the greatest.