Question #5524

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?

Expert's answer

The surface area of a can is

S = 2*pi*R^2 + 2*pi*R*H.

S1 = 2*pi*(2.5/2)^2 + 2*pi*(2.5/2)*5 ≈ 49.0874 square inches;

S2 = 2*pi*(3/2)^2 + 2*pi*(3/2)*4 ≈ 51.8363 square inches.

S1<S2, so the second can need more aluminum to manufacture.

S = 2*pi*R^2 + 2*pi*R*H.

S1 = 2*pi*(2.5/2)^2 + 2*pi*(2.5/2)*5 ≈ 49.0874 square inches;

S2 = 2*pi*(3/2)^2 + 2*pi*(3/2)*4 ≈ 51.8363 square inches.

S1<S2, so the second can need more aluminum to manufacture.

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