A) \[28\pi \,sq.\,\]units
B) 88 sq. units
C) \[88\pi \,sq.\] units
D) \[4\pi \,sq.\] units
Correct Answer: A
Solution :
Let \[{{r}_{1}}\]and \[{{r}_{2}}\]be radii of two spheres. According to question, \[\frac{\frac{4}{3}\pi r_{1}^{3}}{\frac{4}{3}\pi r_{2}^{3}}=\frac{64}{27}\Rightarrow {{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{3}}=\frac{64}{27}\Rightarrow \frac{{{r}_{1}}}{{{r}_{2}}}=\frac{4}{3}\] ?(i) Given, \[{{r}_{1}}+{{r}_{2}}=7\] From (i) and (ii), we get \[{{r}_{1}}=4\]units, \[{{r}_{2}}=3\]units \[\therefore \]Required difference \[=4\pi r_{1}^{2}-4\pi r_{2}^{2}\] \[=4\pi ({{4}^{2}}-{{3}^{2}})=4\pi \times 7=28\pi \,sq.\]units.
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