The sides of a cuboid are in the ratio 3 : 4 : 5 and its surface area is equal to the surface area of the cube with side 6 units. What is the approximate volume of the cuboid?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 210.
The surface area of a cuboid is equal to the surface area of the cube with side 6 units.
Let the sides of the cuboid be 3x, 4x, and 5x
Surface area of a cube = 6 × side2
Surface area of a cuboid = 2(lb + bh + hl)
the volume of a cuboid = lbh
where, l = length, b = width, h = height of a cuboid
According to the question
⇒ 2 × 3x × 4x + 2 × 4x × 5x + 2 × 5x × 3x = 6 × 62
⇒ 24x2 + 40x2 + 30x2 = 216
⇒ 94x2 = 216
⇒ x2 = 216/94
⇒ x2 = 2.297
⇒ x ≈ 1.5159
Hence, the volume of the cuboid = 3x × 4x × 5x = 60 × 1.51593 ≈ 210 cubic units.