Question
The length, breadth and height of a cuboid are in ratio
of 3 : 4 : 5. If the volume of the cuboid is 1620 m3 , find the total surface area of the cuboid.Solution
Volume = length × breadth × height 1620 = 3x × 4x × 5x ⇒ 1620 = 60x3 ⇒ x3 = 27 ⇒ x = 3 Length = 3x = 3 × 3 = 9 m Breadth = 4x = 4 × 3 = 12 m Height = 5x = 5 × 3 = 15 m Total surface area = 2(lb + bh + hl) ⇒ Total surface area = 2(9 × 12 + 12 × 15 + 15 × 9) ⇒ Total surface area = 2(108 + 180 + 135) ⇒ Total surface area = 2(423) ⇒ Total surface area = 846 m2
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