A) \[25%,\]
B) \[48.75%\]
C) \[50%\]
D) \[56.25%\]
Correct Answer: D
Solution :
Let the original edge of the cube be 'a' units. Surface area \[=6{{a}^{2}}\]sq. units Increase in edge = 25% New edge \[=\frac{125}{100}a=\frac{5a}{4}\]units New surface area \[=6\times {{\left( \frac{5a}{4} \right)}^{2}}=\frac{75{{a}^{2}}}{8}\] Increase in surface area \[=\left( \frac{75{{a}^{2}}}{8}-6{{a}^{2}} \right)\,\,\,\,=\frac{27{{a}^{2}}}{8}\] \[\therefore \] Percentage increase in surface area \[=\left( \frac{27{{a}^{2}}}{8}\times \frac{1}{6{{a}^{2}}}\times 100 \right)%=56.25%\]
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