The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 7 cm longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line M) is 28 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
= 28 + 7
= 35 cm
Area of the big semicircle above the dotted line
= 3.14 x 35 x 35 x
12 = 1923.25 cm
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 28 x 28 x
12 = 1230.88 cm
2 Shaded area above the dotted line
= 1923.25 - 1230.88
= 692.37 cm
2 Radius of the small semicircle below the dotted line
= 28 - 7
= 21 cm
Area of the small semicircle below the dotted line
= 3.14 x 21 x 21 x 28
= 692.37 cm
2 Shaded area below the dotted line
= 1230.88 - 692.37
= 538.51 cm
2 Total shaded area
= 692.37 + 538.51
= 1230.88 cm
2 (b)
28 x 4 = 112 cm
Circumference of the curved lines
= 3.14 x 112
= 351.68 cm
Perimeter of the shaded area
= 351.68 + (7 x 2)
= 351.68 + 14
= 365.68 cm
Answer(s): (a) 1230.88 cm
2; (b) 365.68 cm