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12(b) Range of Cuboid Surface Area

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10/23/2025
Problem
The cuboid has sides 5 cm, 6 cm, and 3 cm, each correct to the nearest 1 cm. Find the range of the actual total surface area of the cuboid.
Solution

Hints:

94 cm² to 141 cm²

Surface area = 2(ab + bc + ca). Lower limits: a = 4.5 \\text{ cm}, b = 5.5 \\text{ cm}, c = 2.5 \\text{ cm}. SA = 2(4.5 \\times 5.5 + 5.5 \\times 2.5 + 4.5 \\times 2.5) = 2(24.75 + 13.75 + 11.25) = 94 \\text{ cm}^2. Upper limits: a = 5.5 \\text{ cm}, b = 6.5 \\text{ cm}, c = 3.5 \\text{ cm}. SA = 2(5.5 \\times 6.5 + 6.5 \\times 3.5 + 5.5 \\times 3.5) = 2(35.75 + 22.75 + 19.25) = 141 \\text{ cm}^2.

Tags

measurement
surface area
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