If the area of the region $$\left\{ {(x,y):{x^{{2 \over 3}}} + {y^{{2 \over 3}}} \le 1,\,x + y \ge 0,\,y \ge 0} \right\}$$ is A, then $${{256A} \over \pi }$$ is equal to __________.

$${A_1} = \left\{ {(x,y):|x| \le {y^2},|x| + 2y \le 8} \right\}$$ and

$${A_2} = \left\{ {(x,y):|x| + |y| \le k} \right\}$$. If 27 (Area A₁) = 5 (Area A₂), then k is equal to :

The area (in sq. units) of the region enclosed between the parabola y² = 2x and the line x + y = 4 is __________.

Let S be the region bounded by the curves y = x³ and y² = x. The curve y = 2|x| divides S into two regions of areas R₁, R₂. If max {R₁, R₂} = R₂, then $${{{R_2}} \over {{R_1}}}$$ is equal to ______________.