The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 4 cm longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line C) is 40 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
= 40 + 4
= 44 cm
Area of the big semicircle above the dotted line
= 3.14 x 44 x 44 x
12 = 3039.52 cm
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 40 x 40 x
12 = 2512 cm
2 Shaded area above the dotted line
= 3039.52 - 2512
= 527.52 cm
2 Radius of the small semicircle below the dotted line
= 40 - 4
= 36 cm
Area of the small semicircle below the dotted line
= 3.14 x 36 x 36 x 40
= 527.52 cm
2 Shaded area below the dotted line
= 2512 - 527.52
= 1984.48 cm
2 Total shaded area
= 527.52 + 1984.48
= 2512 cm
2 (b)
40 x 4 = 160 cm
Circumference of the curved lines
= 3.14 x 160
= 502.4 cm
Perimeter of the shaded area
= 502.4 + (4 x 2)
= 502.4 + 8
= 510.4 cm
Answer(s): (a) 2512 cm
2; (b) 510.4 cm