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 :
Options:
A . 5 Times
B . 6 Times
C . 12 Times
D . 17 Times
Answer: Option D 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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