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 W) is 30 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
= 30 + 8
= 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 30 x 30 x
12 = 1413 cm
2 Shaded area above the dotted line
= 2267.08 - 1413
= 854.08 cm
2 Radius of the small semicircle below the dotted line
= 30 - 8
= 22 cm
Area of the small semicircle below the dotted line
= 3.14 x 22 x 22 x 30
= 854.08 cm
2 Shaded area below the dotted line
= 1413 - 854.08
= 558.92 cm
2 Total shaded area
= 854.08 + 558.92
= 1413 cm
2 (b)
30 x 4 = 120 cm
Circumference of the curved lines
= 3.14 x 120
= 376.8 cm
Perimeter of the shaded area
= 376.8 + (8 x 2)
= 376.8 + 16
= 392.8 cm
Answer(s): (a) 1413 cm
2; (b) 392.8 cm