The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 8 m longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line X) is 24 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
= 24 + 8
= 32 m
Area of the big semicircle above the dotted line
= 3.14 x 32 x 32 x
12 = 1607.68 m
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 24 x 24 x
12 = 904.32 m
2 Shaded area above the dotted line
= 1607.68 - 904.32
= 703.36 m
2 Radius of the small semicircle below the dotted line
= 24 - 8
= 16 m
Area of the small semicircle below the dotted line
= 3.14 x 16 x 16 x 24
= 703.36 m
2 Shaded area below the dotted line
= 904.32 - 703.36
= 200.96 m
2 Total shaded area
= 703.36 + 200.96
= 904.32 m
2 (b)
24 x 4 = 96 m
Circumference of the curved lines
= 3.14 x 96
= 301.44 m
Perimeter of the shaded area
= 301.44 + (8 x 2)
= 301.44 + 16
= 317.44 m
Answer(s): (a) 904.32 m
2; (b) 317.44 m