| The length, breadth and height of a cuboid are in the ratio 1: 2: 3. If they are increased by 100%, 200% and 200% respectively, then compared to the original volume the increase in the volume of the cuboid will be |
| [SSC (CGL) 2007] |
A) 5 times
B) 18 times
C) 12 times
D) 17 times
Correct Answer: D
Solution :
| Net increase in volume |
| \[=\left( a+b+c+\frac{ab+bc+ac}{100}+\frac{abc}{100\times 100} \right)\] |
| Here, \[a=100,\]\[b=200\] and \[c=200\] |
| Net increase |
| \[=\left( \frac{\begin{align} & 100+200+200+(100\times 200) \\ & \,\,\,\,\,\,\,\,\,\,\,+(200\times 200)+(100\times 200) \\ \end{align}}{100}+\frac{100\times 200\times 200}{100\times 100} \right)\] |
| = 500 + 800 + 400 = 1700% |
| Now,\[1700\times \frac{1}{100}=17\,\,\text{times}\] |
| Hence, volume of cuboid increases by 17 times. |
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