Question

The boundary of the shaded region in the given diagram consists of three semicircular areas, the smaller ones being equal and it’s diameter 5 cm, if the diameter of the larger one is 10 cm,
calculate:
(i) The length of the boundary,
(ii) The area of the shaded region.     (Take π = 3.14)

Answer 1

(i) Diameter = 10 cm
∴ Radius (r) = `10/2` cm = 5 cm.

Length of the boundary = π(5) + π(2.5) + π(2.5)
= 10π
= 10 x 3.14 cm
= 31.4 cm

(ii) Area of the shaded region
= `1/2 π(5)^2 - 1/2 π(2.5)^2 + 1/2 π(2.5)^2`

= `25/2 π  = 25/2 xx 3.14`

= 25 x 1.57 = 39.25 cm².