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 Q) is 32 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
= 32 + 9
= 41 m
Area of the big semicircle above the dotted line
= 3.14 x 41 x 41 x
12 = 2639.17 m
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 32 x 32 x
12 = 1607.68 m
2 Shaded area above the dotted line
= 2639.17 - 1607.68
= 1031.49 m
2 Radius of the small semicircle below the dotted line
= 32 - 9
= 23 m
Area of the small semicircle below the dotted line
= 3.14 x 23 x 23 x 32
= 1031.49 m
2 Shaded area below the dotted line
= 1607.68 - 1031.49
= 576.19 m
2 Total shaded area
= 1031.49 + 576.19
= 1607.68 m
2 (b)
32 x 4 = 128 m
Circumference of the curved lines
= 3.14 x 128
= 401.92 m
Perimeter of the shaded area
= 401.92 + (9 x 2)
= 401.92 + 18
= 419.92 m
Answer(s): (a) 1607.68 m
2; (b) 419.92 m