The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 8 cm longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line D) is 22 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
= 22 + 8
= 30 cm
Area of the big semicircle above the dotted line
= 3.14 x 30 x 30 x
12 = 1413 cm
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 22 x 22 x
12 = 759.88 cm
2 Shaded area above the dotted line
= 1413 - 759.88
= 653.12 cm
2 Radius of the small semicircle below the dotted line
= 22 - 8
= 14 cm
Area of the small semicircle below the dotted line
= 3.14 x 14 x 14 x 22
= 653.12 cm
2 Shaded area below the dotted line
= 759.88 - 653.12
= 106.76 cm
2 Total shaded area
= 653.12 + 106.76
= 759.88 cm
2 (b)
22 x 4 = 88 cm
Circumference of the curved lines
= 3.14 x 88
= 276.32 cm
Perimeter of the shaded area
= 276.32 + (8 x 2)
= 276.32 + 16
= 292.32 cm
Answer(s): (a) 759.88 cm
2; (b) 292.32 cm