BestDrinks manufactures aluminum cans of pop in two sizes. Can A has a diameter of 2.5 inches and a height of 5 inches.Can B has a diameter of 3 inches and a height of 4 inches. Which can requires more aluminum to manufacture?(Enter only the letter of the correct can in the box.)
Question
BestDrinks manufactures aluminum cans of pop in two sizes. Can A has a diameter of 2.5 inches and a height of 5 inches.Can B has a diameter of 3 inches and a height of 4 inches. Which can requires more aluminum to manufacture?(Enter only the letter of the correct can in the box.)
Solution
To answer this question, we need to calculate the surface area of both cans. The formula for the surface area of a cylinder (which is the shape of a can) is 2πr(h + r), where r is the radius and h is the height.
For Can A: The radius is half the diameter, so r = 2.5/2 = 1.25 inches. The height is 5 inches. So, the surface area of Can A = 2π(1.25)(5 + 1.25) = 2π(1.25)(6.25) = 15.625π square inches.
For Can B: The radius is half the diameter, so r = 3/2 = 1.5 inches. The height is 4 inches. So, the surface area of Can B = 2π(1.5)(4 + 1.5) = 2π(1.5)(5.5) = 16.5π square inches.
Since 16.5π is greater than 15.625π, Can B requires more aluminum to manufacture. So, the answer is B.
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