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Question

The inside perimeter of a running track (shown in the following figure) is 400 m. The length of each of the straight portion is 90 m and the ends are semi-circles. If the track is everywhere 14 m wide. find the area of the track. Also find the length of the outer running track.


Solution

It is given that, and

We know that the circumference C of semicircle of radius be r is

C=πr

The inside perimeter of running track is the sum of twice the length of straight portion and circumferences of semicircles. So,
inside perimeter of running track = 400 m
2l+2πr=400 m
2×90+2×227×r=400 m
r=220×72×22=35 m
Thus, radius of inner semicircle is 35 m.

Now,
radius of outer semi circle r' = 35 + 14 = 49 m

Area of running track = 2×Area of rectangle+2×Area of outer semi circle-2×Area of inner semicircle
            =2×90×14+2×π(49)22-2×π(35)22
            =2520+π×49+3549-35
            =2520+227×84×14
            =2520+3696=6216 m2
Hence, the area of running track = 6216 m2

Now, length L of outer running track is
L = 2 × l + 2πr'
   =2×90+2π×49

   =180+2×227×49
   =180+308=488 m
   
Hence, the length L of outer running track is 488 m.
 


Mathematics
RD Sharma (2020, 2021)
All

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