The edges of a rectangular box are in the ratio of 3 : 5 : 8, and its surface area is 632 cm2. What will be the volume of the box?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 960 cm3.
Given that, Surface area of box = 632 cm2
Ratio of the edges of box = 3 : 5 : 8
Surface area of cuboid = 2(lb + bh + hl)
Volume of cuboid = lbh
Let the length, breadth and height og the box be 3x, 5x and 8x respectively.
According to the given question,
2(lb + bh + hl) = 632
⇒ 2(3x × 5x + 5x × 8x + 8x × 3x) = 632
⇒ 15x2 + 40x2 + 24x2 = 316
⇒ 79x2 = 316
⇒ x2 = 4
⇒ x = 2
Now, l = 6 cm
b = 10 cm
h = 16 cm
Volume of box = 6 × 10 × 16
⇒ 960
Hence the volume of the box is 960 cm3.