8th Class Mental Ability Mensuration Question Bank Mensuration

  • question_answer A large cube is formed from the material obtained by melting three smaller cubes of side 3, 4 and 5 cm. What is the ratio of the total surface areas of the smaller cubes and the large cube?

    A) \[2:1\]                   

    B)       \[3:2\]

    C) \[25:18\]  

    D)                   \[27:20\]

    E) None of these

    Correct Answer: C

    Solution :

    Explanation Option [c] is correct. Volume of the large cube \[=({{3}^{3}}+{{4}^{3}}+{{5}^{3}})=216\,c{{m}^{3}}\] Let the edge of the large cube be a So, \[{{a}^{3}}~=216\Rightarrow ~a=6\text{ }cm\] \[\therefore \] Required ratio = \[\left( \frac{6\times \left( {{3}^{2}}+{{4}^{2}}+{{5}^{2}} \right)}{6\times {{6}^{2}}} \right)=\frac{50}{36}=25:18\]             

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