| If each side of a cube is increased by 10%, then the volume of the cube will be increased |
| [SSC (CGL) Mains 2014] |
A) 30%
B) 10%
C) 33.1%
D) 25%
Correct Answer: C
Solution :
| Suppose, each side of cube \[=a\,\,\text{unit}\] |
| \[\therefore \] Volume of cube \[={{a}^{3}}.\] |
| Now, new side of cube\[=a\times \frac{110}{100}=1.1\,\,a\,\,\text{unit}\] |
| \[\therefore \]New volume of cube \[={{(1.1a)}^{3}}=1.331\,\,a\] |
| \[\therefore \]Required increase percentage |
| \[=\frac{1.331\,\,{{a}^{3}}-{{a}^{3}}}{{{a}^{3}}}\times 100\] |
| \[=\frac{0.331\,\,{{a}^{3}}}{{{a}^{3}}}\times 100=33.1\]% |
| Alternate Method |
| Increase in each side \[=x=y=z=10\]% |
| \[\therefore \]Total increase |
| \[=\left[ x+y+z+\frac{xy+yz+zx}{100}+\frac{xyz}{{{(100)}^{2}}} \right]\]% |
| \[=3x+\frac{3{{x}^{2}}}{100}+\frac{{{x}^{3}}}{{{(100)}^{2}}}\] |
| \[=30+\frac{300}{100}+\frac{1000}{10000}\] |
| \[=30+3+0.1=33.1\]% |
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