The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 3 m longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line L) is 30 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
= 30 + 3
= 33 m
Area of the big semicircle above the dotted line
= 3.14 x 33 x 33 x
12 = 1709.73 m
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 30 x 30 x
12 = 1413 m
2 Shaded area above the dotted line
= 1709.73 - 1413
= 296.73 m
2 Radius of the small semicircle below the dotted line
= 30 - 3
= 27 m
Area of the small semicircle below the dotted line
= 3.14 x 27 x 27 x 30
= 296.73 m
2 Shaded area below the dotted line
= 1413 - 296.73
= 1116.27 m
2 Total shaded area
= 296.73 + 1116.27
= 1413 m
2 (b)
30 x 4 = 120 m
Circumference of the curved lines
= 3.14 x 120
= 376.8 m
Perimeter of the shaded area
= 376.8 + (3 x 2)
= 376.8 + 6
= 382.8 m
Answer(s): (a) 1413 m
2; (b) 382.8 m