10th Class Mathematics Mensuration Question Bank Mensuration

  • question_answer
    The percentage increase in the surface area of a cube, when each side is increased to \[\frac{3}{2}\] times the original length is

    A)  225                 

    B)         200

    C)  175                       

    D)  125  

    Correct Answer: D

    Solution :

     Let side of the cube be x. Then its total surface area \[=6{{x}^{2}}\] If each side is increased to\[\frac{3}{2}x,\] then total surface area \[=6\times \frac{3x}{2}\times \frac{3x}{2}=\frac{27{{x}^{2}}}{2}\] \[\therefore \]  Increase  \[=\frac{27{{x}^{2}}}{2}-6{{x}^{2}}=\frac{15{{x}^{2}}}{2}\] \[\therefore \] % increase \[=\frac{15{{x}^{2}}}{2}\times \frac{100}{6{{x}^{2}}}=125\]


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