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 cm longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line C) is 18 cm.
- 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
= 18 + 8
= 26 cm
Area of the big semicircle above the dotted line
= 3.14 x 26 x 26 x
12 = 1061.32 cm
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 18 x 18 x
12 = 508.68 cm
2 Shaded area above the dotted line
= 1061.32 - 508.68
= 552.64 cm
2 Radius of the small semicircle below the dotted line
= 18 - 8
= 10 cm
Area of the small semicircle below the dotted line
= 3.14 x 10 x 10 x 18
= 552.64 cm
2 Shaded area below the dotted line
= 508.68 - 552.64
= -43.96 cm
2 Total shaded area
= 552.64 + -43.96
= 508.68 cm
2 (b)
18 x 4 = 72 cm
Circumference of the curved lines
= 3.14 x 72
= 226.08 cm
Perimeter of the shaded area
= 226.08 + (8 x 2)
= 226.08 + 16
= 242.08 cm
Answer(s): (a) 508.68 cm
2; (b) 242.08 cm