The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 3 cm longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line T) 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 + 3
= 21 cm
Area of the big semicircle above the dotted line
= 3.14 x 21 x 21 x
12 = 692.37 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
= 692.37 - 508.68
= 183.69 cm
2 Radius of the small semicircle below the dotted line
= 18 - 3
= 15 cm
Area of the small semicircle below the dotted line
= 3.14 x 15 x 15 x 18
= 183.69 cm
2 Shaded area below the dotted line
= 508.68 - 183.69
= 324.99 cm
2 Total shaded area
= 183.69 + 324.99
= 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 + (3 x 2)
= 226.08 + 6
= 232.08 cm
Answer(s): (a) 508.68 cm
2; (b) 232.08 cm