The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 5 m longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line Y) is 38 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
= 38 + 5
= 43 m
Area of the big semicircle above the dotted line
= 3.14 x 43 x 43 x
12 = 2902.93 m
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 38 x 38 x
12 = 2267.08 m
2 Shaded area above the dotted line
= 2902.93 - 2267.08
= 635.85 m
2 Radius of the small semicircle below the dotted line
= 38 - 5
= 33 m
Area of the small semicircle below the dotted line
= 3.14 x 33 x 33 x 38
= 635.85 m
2 Shaded area below the dotted line
= 2267.08 - 635.85
= 1631.23 m
2 Total shaded area
= 635.85 + 1631.23
= 2267.08 m
2 (b)
38 x 4 = 152 m
Circumference of the curved lines
= 3.14 x 152
= 477.28 m
Perimeter of the shaded area
= 477.28 + (5 x 2)
= 477.28 + 10
= 487.28 m
Answer(s): (a) 2267.08 m
2; (b) 487.28 m