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 N) 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 + 5
= 33 cm
Area of the big semicircle above the dotted line
= 3.14 x 33 x 33 x
12 = 1709.73 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
= 1709.73 - 1230.88
= 478.85 cm
2 Radius of the small semicircle below the dotted line
= 28 - 5
= 23 cm
Area of the small semicircle below the dotted line
= 3.14 x 23 x 23 x 28
= 478.85 cm
2 Shaded area below the dotted line
= 1230.88 - 478.85
= 752.03 cm
2 Total shaded area
= 478.85 + 752.03
= 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 + (5 x 2)
= 351.68 + 10
= 361.68 cm
Answer(s): (a) 1230.88 cm
2; (b) 361.68 cm