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 200%, 300% and 300%, respectively. Then compared to the original volume, the increase in the volume of the cuboid will be :

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 20 Jul 2023 Shift 4)

Answer 1

Given:

The length, breadth and height of a cuboid are in the ratio 1 : 2 : 3.

Formula used:

Volume of cuboid = Length(L) × Breadth(B) × Height(H)

Calculation:

Let the Length, breadth and height of the cuboid be 100, 200, and 300 respectively.

Volume of cuboid = 100 × 200 × 300 = 6000000

Length increased by 200%, Breadth increase by 300% and height by 300%

Now, new length = 300, breadth = 800 and height = 1200 respectively

⇒ new volume of cuboid = 300 × 800 × 1200

= 288000000

Increase in volume = (new volume of the cuboid – the volume of the cuboid)/volume of the cuboid

= (288000000 – 6000000)/6000000

= 282000000/6000000

= 47 times

∴ The increase in the volume of the cuboid will be 47 times.