The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 7 cm longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line Q) is 40 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
= 40 + 7
= 47 cm
Area of the big semicircle above the dotted line
= 3.14 x 47 x 47 x
12 = 3468.13 cm
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 40 x 40 x
12 = 2512 cm
2 Shaded area above the dotted line
= 3468.13 - 2512
= 956.13 cm
2 Radius of the small semicircle below the dotted line
= 40 - 7
= 33 cm
Area of the small semicircle below the dotted line
= 3.14 x 33 x 33 x 40
= 956.13 cm
2 Shaded area below the dotted line
= 2512 - 956.13
= 1555.87 cm
2 Total shaded area
= 956.13 + 1555.87
= 2512 cm
2 (b)
40 x 4 = 160 cm
Circumference of the curved lines
= 3.14 x 160
= 502.4 cm
Perimeter of the shaded area
= 502.4 + (7 x 2)
= 502.4 + 14
= 516.4 cm
Answer(s): (a) 2512 cm
2; (b) 516.4 cm