The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 9 m longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line T) is 40 m.
- Find the area of the shaded part.
- Find the perimeter of the dotted line. (Take π = 3.14)
(a)
Radius of the big semicircle above the dotted line
= 40 + 9
= 49 m
Area of the big semicircle above the dotted line
= 3.14 x 49 x 49 x
12 = 3769.57 m
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 40 x 40 x
12 = 2512 m
2 Shaded area above the dotted line
= 3769.57 - 2512
= 1257.57 m
2 Radius of the small semicircle below the dotted line
= 40 - 9
= 31 m
Area of the small semicircle below the dotted line
= 3.14 x 31 x 31 x 40
= 1257.57 m
2 Shaded area below the dotted line
= 2512 - 1257.57
= 1254.43 m
2 Total shaded area
= 1257.57 + 1254.43
= 2512 m
2 (b)
40 x 4 = 160 m
Circumference of the curved lines
= 3.14 x 160
= 502.4 m
Perimeter of the shaded area
= 502.4 + (9 x 2)
= 502.4 + 18
= 520.4 m
Answer(s): (a) 2512 m
2; (b) 520.4 m