The surface area of a cuboid is 468 cm2, and its dimensions are in the ratio 2 : 3 : 4. Find its volume.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 648 cm3.
Let the dimensions of the cuboid 2x, 3x, 4x
Surface area = 2[(2x × 3x) + (3x × 4x) + (4x × 2x)]
= 2[6x2 + 12x2 + 8x2]
= 2[26x2]
= 52x2
So, 52x2 = 468
⇒ x2 = 468/52 = 9
⇒ x3 = 27
Volume = 2x × 3x × 4x = 24x3 = 24 × 27 = 648 cm3