Areas related to Circles ncert solutions Chapter 12 Exercise 12.3 Question 8
8. Fig depicts a racing track whose left and right ends are semi-circular.
The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If, the track is 10 m wide, find:
(i) the distance around the track along its inner edge.
(ii) the area of the track.
Radius of inner semi-circle = m
Circumference of inner semicircle m
The distance around the track along its inner edge=length of two inner parallel lines each equal to 106 m + circumference of two inner semicircles.
Area of the track = area of two rectangles formed in the track + area enclosed by the semi-circles (1)
Area of rectangle = length x breadth = 106 x width of track = 106 x 10=1060 m
Area of two rectangles=2 x 1060=2120 m (2)
Diameter of bigger semi-circle=60+width of track + width of track=60+10+10=80 m
Radius of bigger semi-circle m
Area enclosed by left semi-circles=Area of bigger semi-circle-area of smaller semi-circle
Area enclosed by left and right semi-circles=2 x 1100=2200 (3)
Putting (2) and (3) in (1), we get
Area of the track = area of two rectangles formed in the track + area enclosed by the semi-circles