The figure is not drawn to scale. It is formed by quadrants and semicircles of two sizes. The radius of the larger quadrant is 4 cm longer than the radius of the smaller quadrant. The radius of the smaller quadrant (Line S) is 30 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
= 30 + 4
= 34 cm
Area of the big semicircle above the dotted line
= 3.14 x 34 x 34 x
12 = 1814.92 cm
2 Area of the small semicircle above the dotted line
= Area of the big semicircle below the dotted line
= 3.14 x 30 x 30 x
12 = 1413 cm
2 Shaded area above the dotted line
= 1814.92 - 1413
= 401.92 cm
2 Radius of the small semicircle below the dotted line
= 30 - 4
= 26 cm
Area of the small semicircle below the dotted line
= 3.14 x 26 x 26 x 30
= 401.92 cm
2 Shaded area below the dotted line
= 1413 - 401.92
= 1011.08 cm
2 Total shaded area
= 401.92 + 1011.08
= 1413 cm
2 (b)
30 x 4 = 120 cm
Circumference of the curved lines
= 3.14 x 120
= 376.8 cm
Perimeter of the shaded area
= 376.8 + (4 x 2)
= 376.8 + 8
= 384.8 cm
Answer(s): (a) 1413 cm
2; (b) 384.8 cm