The length, breadth, and height of a cuboid are in the ratio of 3 : 4 : 5. If the volume of the cuboid is 1620 m3, find the total surface area of the cuboid.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 846 m2.
Let the length be 3x, the breadth be 4x, and the height be 5x
Volume of a cuboid = length × breadth × height
So, (3x) × (4x) × (5x) = 60x3 = 1620
⇒ x3 = 1620/60 = 27
⇒ x = ³√27 = 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 + lh) = 2(9 × 12 + 12 × 15 + 9 × 15) = 2 × 423 = 846
Therefore, the total surface area of the cuboid is 846 m2.