## Areas related to Circles Ncert solutions Chapter 12 Exercise 12.3 Question 8

**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.

**Solution:**

**(i)**

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.

**m**

**(ii)**

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

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