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Question

The following geometrical shapes are made up of paper. ___ required less paper and ___ has more volume.

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Solution

Calculating Surface Area

Surface Area of Cube = 6a2= 6 × 4 × 4 = 96 cm2

Surface Area of Cuboid = 2(lb + bh + hl) = 2(10 × 5 + 5 × 2 + 2 × 10) = 2 × 80 =160 cm2

Surface Area of Cylinder = 2πrh = 2 × 227 × 5 × 14 = 440 cm2.

Least Surface Area = Cube = 96cm2 (cube)

Calculating Volume

Volume of Cube = a3 = 64 cm3

Volume of Cuboid = l × b × h = 10 × 5 × 2 =100 cm3

Volume of Cylinder = πr2h = 227 × 25 × 14 = 1100 cm3

Cylinder has maximum volume = 1100 cm3


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