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 cm longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line Z) is 16 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
= 16 + 5
= 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 16 x 16 x
12 = 401.92 cm
2 Shaded area above the dotted line
= 692.37 - 401.92
= 290.45 cm
2 Radius of the small semicircle below the dotted line
= 16 - 5
= 11 cm
Area of the small semicircle below the dotted line
= 3.14 x 11 x 11 x 16
= 290.45 cm
2 Shaded area below the dotted line
= 401.92 - 290.45
= 111.47 cm
2 Total shaded area
= 290.45 + 111.47
= 401.92 cm
2 (b)
16 x 4 = 64 cm
Circumference of the curved lines
= 3.14 x 64
= 200.96 cm
Perimeter of the shaded area
= 200.96 + (5 x 2)
= 200.96 + 10
= 210.96 cm
Answer(s): (a) 401.92 cm
2; (b) 210.96 cm