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 T) 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 + 8
= 24 cm
Area of the big semicircle above the dotted line
= 3.14 x 24 x 24 x
12 = 904.32 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
= 904.32 - 401.92
= 502.4 cm
2 Radius of the small semicircle below the dotted line
= 16 - 8
= 8 cm
Area of the small semicircle below the dotted line
= 3.14 x 8 x 8 x 16
= 502.4 cm
2 Shaded area below the dotted line
= 401.92 - 502.4
= -100.48 cm
2 Total shaded area
= 502.4 + -100.48
= 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 + (8 x 2)
= 200.96 + 16
= 216.96 cm
Answer(s): (a) 401.92 cm
2; (b) 216.96 cm