A) 0.2695
B) 2.695
C) 3.695
D) 0.3695
Correct Answer: B
Solution :
| \[{{1}^{3}}+{{2}^{3}}+...+{{9}^{3}}=2025\] (Given) |
| Now, \[{{(0.11)}^{3}}+{{(0.22)}^{3}}+...+{{(0.99)}^{3}}\] |
| \[={{\left( \frac{11}{100} \right)}^{3}}+{{\left( \frac{22}{100} \right)}^{3}}+...+{{\left( \frac{99}{100} \right)}^{3}}\] |
| \[={{\left( \frac{11}{100} \right)}^{3}}({{1}^{3}}+{{2}^{3}}+...+{{9}^{3}})=\frac{1331}{1000000}\times 2025\] |
| \[=\frac{2695275}{1000000}=2.695275\approx 2.695\] |
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