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 B) is 32 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
= 32 + 8
= 40 cm
Area of the big semicircle above the dotted line
= 3.14 x 40 x 40 x
12 = 2512 cm
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 32 x 32 x
12 = 1607.68 cm
2 Shaded area above the dotted line
= 2512 - 1607.68
= 904.32 cm
2 Radius of the small semicircle below the dotted line
= 32 - 8
= 24 cm
Area of the small semicircle below the dotted line
= 3.14 x 24 x 24 x 32
= 904.32 cm
2 Shaded area below the dotted line
= 1607.68 - 904.32
= 703.36 cm
2 Total shaded area
= 904.32 + 703.36
= 1607.68 cm
2 (b)
32 x 4 = 128 cm
Circumference of the curved lines
= 3.14 x 128
= 401.92 cm
Perimeter of the shaded area
= 401.92 + (8 x 2)
= 401.92 + 16
= 417.92 cm
Answer(s): (a) 1607.68 cm
2; (b) 417.92 cm