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 Z) is 34 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
= 34 + 4
= 38 cm
Area of the big semicircle above the dotted line
= 3.14 x 38 x 38 x
12 = 2267.08 cm
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 34 x 34 x
12 = 1814.92 cm
2 Shaded area above the dotted line
= 2267.08 - 1814.92
= 452.16 cm
2 Radius of the small semicircle below the dotted line
= 34 - 4
= 30 cm
Area of the small semicircle below the dotted line
= 3.14 x 30 x 30 x 34
= 452.16 cm
2 Shaded area below the dotted line
= 1814.92 - 452.16
= 1362.76 cm
2 Total shaded area
= 452.16 + 1362.76
= 1814.92 cm
2 (b)
34 x 4 = 136 cm
Circumference of the curved lines
= 3.14 x 136
= 427.04 cm
Perimeter of the shaded area
= 427.04 + (4 x 2)
= 427.04 + 8
= 435.04 cm
Answer(s): (a) 1814.92 cm
2; (b) 435.04 cm