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 S) is 16 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
= 16 + 3
= 19 cm
Area of the big semicircle above the dotted line
= 3.14 x 19 x 19 x
12 = 566.77 cm
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 16 x 16 x
12 = 401.92 cm
2 Shaded area above the dotted line
= 566.77 - 401.92
= 164.85 cm
2 Radius of the small semicircle below the dotted line
= 16 - 3
= 13 cm
Area of the small semicircle below the dotted line
= 3.14 x 13 x 13 x 16
= 164.85 cm
2 Shaded area below the dotted line
= 401.92 - 164.85
= 237.07 cm
2 Total shaded area
= 164.85 + 237.07
= 401.92 cm
2 (b)
16 x 4 = 64 cm
Circumference of the curved lines
= 3.14 x 64
= 200.96 cm
Perimeter of the shaded area
= 200.96 + (3 x 2)
= 200.96 + 6
= 206.96 cm
Answer(s): (a) 401.92 cm
2; (b) 206.96 cm