The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 3 cm longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line R) is 36 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
= 36 + 3
= 39 cm
Area of the big semicircle above the dotted line
= 3.14 x 39 x 39 x
12 = 2387.97 cm
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 36 x 36 x
12 = 2034.72 cm
2 Shaded area above the dotted line
= 2387.97 - 2034.72
= 353.25 cm
2 Radius of the small semicircle below the dotted line
= 36 - 3
= 33 cm
Area of the small semicircle below the dotted line
= 3.14 x 33 x 33 x 36
= 353.25 cm
2 Shaded area below the dotted line
= 2034.72 - 353.25
= 1681.47 cm
2 Total shaded area
= 353.25 + 1681.47
= 2034.72 cm
2 (b)
36 x 4 = 144 cm
Circumference of the curved lines
= 3.14 x 144
= 452.16 cm
Perimeter of the shaded area
= 452.16 + (3 x 2)
= 452.16 + 6
= 458.16 cm
Answer(s): (a) 2034.72 cm
2; (b) 458.16 cm