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 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 + 5
= 27 cm
Area of the big semicircle above the dotted line
= 3.14 x 27 x 27 x
12 = 1144.53 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
= 1144.53 - 759.88
= 384.65 cm
2 Radius of the small semicircle below the dotted line
= 22 - 5
= 17 cm
Area of the small semicircle below the dotted line
= 3.14 x 17 x 17 x 22
= 384.65 cm
2 Shaded area below the dotted line
= 759.88 - 384.65
= 375.23 cm
2 Total shaded area
= 384.65 + 375.23
= 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 + (5 x 2)
= 276.32 + 10
= 286.32 cm
Answer(s): (a) 759.88 cm
2; (b) 286.32 cm