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 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 + 9
= 27 cm
Area of the big semicircle above the dotted line
= 3.14 x 27 x 27 x
12 = 1144.53 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
= 1144.53 - 508.68
= 635.85 cm
2 Radius of the small semicircle below the dotted line
= 18 - 9
= 9 cm
Area of the small semicircle below the dotted line
= 3.14 x 9 x 9 x 18
= 635.85 cm
2 Shaded area below the dotted line
= 508.68 - 635.85
= -127.17 cm
2 Total shaded area
= 635.85 + -127.17
= 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 + (9 x 2)
= 226.08 + 18
= 244.08 cm
Answer(s): (a) 508.68 cm
2; (b) 244.08 cm