Let $A_1, A_2$ and $A_3$ be the regions on $R^2$ defined by

$A_1=\left\{\left(x,y\right):x\ge 0,y\ge 0,2x+2y-x^2-y^2>1>x+y\right\}$

$A_2=\left\{\left(x,y\right):x\ge 0,y\ge 0,x+y>1>x^2+y^2\right\}$

$A_3=\left\{\left(x,y\right):x\ge 0,y\ge 0,x+y>1>x^3+y^3\right\}$

Denote by $\left|A_1\right|, \left|A_2\right|$ and $\left|A_3\right|$ the areas of the regions $A_1, A_2$ and $A_3$ respectively. Then

• A

  $\left|A_1\right|>\left|A_2\right|>\left|A_3\right|$
• B

  $\left|A_1\right|>\left|A_3\right|>\left|A_2\right|$
• Correct answer
  C

  $\left|A_1\right|=\left|A_2\right|<\left|A_3\right|$
• D

  $\left|A_1\right|=\left|A_3\right|>\left|A_2\right|$

Hence, the correct answer is option: 'C'.