Question
The lateral surface area of a cube is 324 cm2
. The length of a cuboid is 50% more than the side of the cube. The breadth of the cuboid is 5 cm less than its length and 20% less than its height. Find the total surface area of the cuboid.Solution
Let the length of the cube be ‘a’ cm
According to the question,
4a2 = 324
=> a2 = 81
=> a = 9
Therefore, length of the cuboid = l = 1.5 × 9 = 13.5 cm
Breadth of the cuboid = b = 13.5 – 5 = 8.5 cm
Height of the cuboid = h = 8.5/0.8 = 10.625 cm
Therefore, total surface area of the cuboid = 2(lb + bh + lh) = 2 × {(13.5 × 8.5) + (8.5 × 10.625) + (13.5 × 10.625)} = 697 cm2
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