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 R) is 38 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
= 38 + 8
= 46 cm
Area of the big semicircle above the dotted line
= 3.14 x 46 x 46 x
12 = 3322.12 cm
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 38 x 38 x
12 = 2267.08 cm
2 Shaded area above the dotted line
= 3322.12 - 2267.08
= 1055.04 cm
2 Radius of the small semicircle below the dotted line
= 38 - 8
= 30 cm
Area of the small semicircle below the dotted line
= 3.14 x 30 x 30 x 38
= 1055.04 cm
2 Shaded area below the dotted line
= 2267.08 - 1055.04
= 1212.04 cm
2 Total shaded area
= 1055.04 + 1212.04
= 2267.08 cm
2 (b)
38 x 4 = 152 cm
Circumference of the curved lines
= 3.14 x 152
= 477.28 cm
Perimeter of the shaded area
= 477.28 + (8 x 2)
= 477.28 + 16
= 493.28 cm
Answer(s): (a) 2267.08 cm
2; (b) 493.28 cm