Question

what would be the radius {r}?!........

Answer 1

See, the smaller semicircles are of diameter 3cm.

So they are symmetrically placed on the diameter of the larger semicircle.

Now, the circle is touching the diameter of larger semicircle and also both the smaller semicircles.

So the circle is also symmetrically placed inside the semicircle.

That means the circle is placed centrally in the semicircle.
So at the top, the circle is touching the top most point of semicircle.

That means radius of semicircle = diameter of circle = 4.5 cm

So r = 4.5/2 = 2.25cm