| A large cube is formed by melting three smaller cubes of 3 cm, 4 cm and 5 cm side. What is the ratio of the total surface areas of the small cubes and the larger cube? |
A) 2 : 1
B) 3 : 2
C) 25 : 18
D) 27 : 20
Correct Answer: C
Solution :
| Volume of largest cube |
| \[={{3}^{3}}+{{4}^{3}}+{{5}^{3}}\] |
| \[=27+64+125=216\,c{{m}^{3}}\] |
| \[\therefore \] Side of largest cube \[=\sqrt[3]{216}=6\,cm\] |
| Total surface area of small cube |
| \[\therefore \] Required ratio |
| \[\text{=}\,\,\frac{\text{Total}\,\text{surface}\,\text{area}\,\text{of}\,\text{small}\,\text{cube}}{\text{Total}\,\text{surface}\,\text{area}\,\text{of}\,\text{largest}\,\text{cube}}\] |
| \[\text{=}\,\,\,\frac{6\times {{(3)}^{2}}+6\times {{(4)}^{2}}+6\times {{(5)}^{2}}}{6\times {{(6)}^{2}}}\] |
| \[=\,\,\,\frac{9+16+25}{36}=\frac{50}{36}=\frac{25}{18}=25:18\] |
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