F.2 maths

Let the centre of the bigger circle be O and that of the smaller circle be Q
4^2+4^2=OQ^2 (Pyth. thm.)
OQ=√32 cm

∴R=√32+4 cm
=5.67+4
=9.67cm (3 sig. sig.)

You had better use the word 'quadrant' instead of 'bigger circle' since 'quadrant' is used in the question and the 'bigger circle' is not really a complete circle.

The radius:
[sqrt(4^2 + 4^2) + 4] cm
= 4[sqrt(2) + 1] cm