The length, breadth, and height of a rectangular box are in the ratio 3:2:4, respectively, and the cost of covering it with a sheet of paper at the rate of ₹1.50 per square metre is ₹1.950. Find 50% of the volume of the box (in m³).
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 1500.
Let dimensions be 3x, 2x, 4x
Surface Area = = 1300 m²
Surface Area of box = 2(lb + bh + hl)
⇒ 2(3x × 2x + 2x × 4x + 4x × 3x)
⇒ 2(6x2 + 8x2 + 12x2) = 52x2
⇒ 52x2 = 1300
⇒ x2 = 25
⇒ x = 5
Volume = 3x × 2x × 4x = 24x3
⇒ 24 × (5)3 = 24 × 125 = 3000 m3
⇒ 50% of volume = 1500 m3