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 V) is 34 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
= 34 + 8
= 42 cm
Area of the big semicircle above the dotted line
= 3.14 x 42 x 42 x
12 = 2769.48 cm
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 34 x 34 x
12 = 1814.92 cm
2 Shaded area above the dotted line
= 2769.48 - 1814.92
= 954.56 cm
2 Radius of the small semicircle below the dotted line
= 34 - 8
= 26 cm
Area of the small semicircle below the dotted line
= 3.14 x 26 x 26 x 34
= 954.56 cm
2 Shaded area below the dotted line
= 1814.92 - 954.56
= 860.36 cm
2 Total shaded area
= 954.56 + 860.36
= 1814.92 cm
2 (b)
34 x 4 = 136 cm
Circumference of the curved lines
= 3.14 x 136
= 427.04 cm
Perimeter of the shaded area
= 427.04 + (8 x 2)
= 427.04 + 16
= 443.04 cm
Answer(s): (a) 1814.92 cm
2; (b) 443.04 cm