Question
The lateral surface area of a cube is 1024 cm2 . The length of a cuboid is 50% more than the side of the cube. The breadth of the cuboid is 15 cm less than its length and 10% 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 = 1024
=> a2 = 256
=> a = 16
Therefore, length of the cuboid = l = 1.5 × 16 = 24 cm
Breadth of the cuboid = b = 24 – 15 = 9 cm
Height of the cuboid = h = 9/0.9 = 10 cm
Therefore, total surface area of the cuboid = 2(lb + bh + lh) = 2 × {(24 × 9) + (9 × 10) + (24 × 10)} = 1092 cm2
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