Answer:
Explanation:
To determine which can will cost more to manufacture, we need to calculate the surface area and the associated costs for each can.
The surface area of a cylindrical can is given by the formula:
Surface Area = 2πr² + 2πrh
For the can with a radius of 5 inches and a height of 4 inches:
Surface Area = 2π(5)² + 2π(5)(4)
= 50π + 40π
= 90π square inches
For the can with a radius of 4 inches and a height of 5 inches:
Surface Area = 2π(4)² + 2π(4)(5)
= 32π + 40π
= 72π square inches
Now, let's calculate the costs for each can:
Cost for tops and bottoms = Surface Area × $1.20 per square inch
For the can with a radius of 5 inches and a height of 4 inches:
Cost for tops and bottoms = 90π × $1.20
≈ $339.29
For the can with a radius of 4 inches and a height of 5 inches:
Cost for tops and bottoms = 72π × $1.20
≈ $271.72
Cost for curved surfaces = (Surface Area - 2πr²) × $0.90 per square inch
For the can with a radius of 5 inches and a height of 4 inches:
Cost for curved surfaces = (90π - 2π(5)²) × $0.90
≈ $225.99
For the can with a radius of 4 inches and a height of 5 inches:
Cost for curved surfaces = (72π - 2π(4)²) × $0.90
≈ $181.79
Finally, we can calculate the total cost for each can:
Total Cost = Cost for tops and bottoms + Cost for curved surfaces
For the can with a radius of 5 inches and a height of 4 inches:
Total Cost = $339.29 + $225.99
≈ $565.28
For the can with a radius of 4 inches and a height of 5 inches:
Total Cost = $271.72 + $181.79
≈ $453.51
Comparing the total costs, we can see that the can with a radius of 5 inches and a height of 4 inches will cost more to manufacture. Therefore, the correct answer is A. The can with a radius of 5 inches and a height of 4 inches will cost more.