The figure is make up of 3 circles. The small circle has centre J and a radius of 6 m. The big circle, has centre J and a radius of 10 m. 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 K, L and M.
- Find the radius of the medium-sized circle.
- Find the area of region M. Use a calculator to obtain the value of π. (Round off to nearest 2 decimal places).
- Express the area of the region L as a ratio to the area of region K.
(a)
Radius of the medium-sized circle
= (
102 -
62) + 6
= 8 m
(b)
Area of the big circle
= π x 10 x 10
= 100π m
2 Area of medium-sized circle
= π x 8 x 8
= 64π m
2 Area of region M
= 100π - 64π
= 36π
≈ 113.10 m
2 (Round off to nearest 2 decimal places).
(c)
L : K
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 m; (b) 113.10 m
2; (c) 9 : 7