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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 :

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 : Correct Answer 17 Times

Let the original length, breadth and height of the cuboid be x, 2x and 3x units respectively
Then, original volume = (x × 2x × 3x) cu.units = 6x3 cu.units
New length = 200% of x = 2x
New breadth = 300% of 2x = 6x
New height = 300% of 3x = 9x
∴ New volume :
= (2x × 6x × 9x) cu.units
= 108x3 cu.units
Increase in volume :
= (108x3 - 6x3) cu.units
= (102x3) cu.units
∴ Required ratio :
$$\eqalign{ & = \frac{{102{{\text{x}}^3}}}{{6{{\text{x}}^3}}} \cr & = 17{\text{ }}\left( {{\text{Times}}} \right) \cr} $$

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