The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 9 cm longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line Q) is 14 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
= 14 + 9
= 23 cm
Area of the big semicircle above the dotted line
= 3.14 x 23 x 23 x
12 = 830.53 cm
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 14 x 14 x
12 = 307.72 cm
2 Shaded area above the dotted line
= 830.53 - 307.72
= 522.81 cm
2 Radius of the small semicircle below the dotted line
= 14 - 9
= 5 cm
Area of the small semicircle below the dotted line
= 3.14 x 5 x 5 x 14
= 522.81 cm
2 Shaded area below the dotted line
= 307.72 - 522.81
= -215.09 cm
2 Total shaded area
= 522.81 + -215.09
= 307.72 cm
2 (b)
14 x 4 = 56 cm
Circumference of the curved lines
= 3.14 x 56
= 175.84 cm
Perimeter of the shaded area
= 175.84 + (9 x 2)
= 175.84 + 18
= 193.84 cm
Answer(s): (a) 307.72 cm
2; (b) 193.84 cm