The figure is make up of 3 circles. The small circle has centre M and a radius of 6 cm. The big circle, has centre M and a radius of 10 cm. The diameter of the big circle cuts through the centre of the medium-sized circle and the small circle. The three regions formed are indicated as N, P and Q.

1. Find the radius of the medium-sized circle.
2. Find the area of region Q. Use a calculator to obtain the value of π. (Round off to nearest 2 decimal places).
3. Express the area of the region P as a ratio to the area of region N.

(a)
Radius of the medium-sized circle
= (¹⁰₂ - ⁶₂) + 6
= 8 cm

(b)
Area of the big circle
= π x 10 x 10
= 100π cm²

Area of medium-sized circle
= π x 8 x 8
= 64π cm²

Area of region Q
= 100π - 64π
= 36π
≈ 113.10 cm² (Round off to nearest 2 decimal places).

(c)
P : N
π x 6 x 6 : (π x 8 x 8) - (π x 6 x 6)
36π : 64π - 36π
36 : 28
9 : 7

Answer(s): (a) 8 cm; (b) 113.10 cm²; (c) 9 : 7