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 V) 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 + 7
= 37 cm
Area of the big semicircle above the dotted line
= 3.14 x 37 x 37 x
12 = 2149.33 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
= 2149.33 - 1413
= 736.33 cm
2 Radius of the small semicircle below the dotted line
= 30 - 7
= 23 cm
Area of the small semicircle below the dotted line
= 3.14 x 23 x 23 x 30
= 736.33 cm
2 Shaded area below the dotted line
= 1413 - 736.33
= 676.67 cm
2 Total shaded area
= 736.33 + 676.67
= 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 + (7 x 2)
= 376.8 + 14
= 390.8 cm
Answer(s): (a) 1413 cm
2; (b) 390.8 cm