$$ABC$$ is a quadrant of a circle of radius 10 cm . Two semicircles are drawn as in the figure.

The area of the shaded portion is $$k\pi$$, where $$k$$ is a positive integer. The value of $$k$$ is

The radius $$AB$$ is 10 cm and the two semicircles stand on its two halves, each of length 5 cm, so the two semicircles have exactly the same area. One of them is cut out of the quadrant while the other is added on outside it, so the two changes cancel. The shaded area is therefore the area of the quadrant, $$\frac{1}{4} \times \pi \times 10^2 = 25\pi$$, giving $$k = 25$$.