A) \[2{{\left( \frac{4}{25} \right)}^{\frac{1}{3}}}\]
B) \[4{{\left( \frac{4}{25} \right)}^{\frac{1}{3}}}\]
C) \[2{{\left( \frac{2}{5} \right)}^{\frac{1}{3}}}\]
D) \[4{{\left( \frac{2}{5} \right)}^{\frac{1}{3}}}\]
Correct Answer: B
Solution :
\[S(\alpha )=\{(x,y):{{y}^{2}}\le x,0\le x\le \alpha \}\] \[A(\alpha )=2\int\limits_{0}^{\alpha }{\sqrt{x}}dx=2{{\alpha }^{\frac{3}{2}}}\] \[A(4)=2\times {{4}^{3/2}}=16\] \[A(\lambda )=2\times {{\lambda }^{3/2}}\] \[\frac{A(\lambda )}{A(4)}=\frac{2}{5}\Rightarrow \lambda =4.{{\left( \frac{4}{25} \right)}^{1/3}}\]
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