# 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 =$\frac{60}{2}=30$ m

Circumference of inner semicircle $=\pi.r=\frac{22}{7} \times 30=\frac{660}{7}$ 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.

$=106+106+\frac{660}{7}+\frac{660}{7}=\frac{2804}{7}$ 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

$\Rightarrow$ 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

$\Rightarrow$ Radius of bigger semi-circle $=\frac{80}{2}=40$ m

Area enclosed by left semi-circles=Area of bigger semi-circle-area of smaller semi-circle $=\frac{\pi.}{2}(r1)^2-\pi.(r2)^2$

$=\frac{\pi}{2}.(r1^2-r2^2)=\frac{\pi}{2}.(40^2-30^2)=\frac{22}{14}(1600-900)=1100$ $m^2$

$\Rightarrow$ Area enclosed by left and right semi-circles=2 x 1100=2200 $m^2$             (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

$=2120+2200=4320$ $m^2$

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