Question

The length, breadth and height of a cuboid are in the ratio 1 : 2 : 3. The length, breadth and height of the cuboid are increased by 100%, 200% and 200% respectively. Then, the increase in the volume of the cuboid is 

(a) 5 times

(b) 6 times

(c) 12 times

(d) 17 times

Answer 1

Correct option is (d) 17 times

Let the length breadth and height of the cuboid be x, 2x and 3x units.

The dimensions after increase are \(x + \frac{100}{100}x, 2x + \frac{200}{100} \times 2x, 3x + \frac{200}{100} \times 3x\)

i.e., 2x, 6x and 9x

Original volume = x × 2x × 3x = 6x³

Increased volume = 2x × 6x × 9x = 108x³

∴ Increase in volume =108x³ − 6x³ = 102x³

= 17 × 6x³

= 17 × original volume