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Question

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


Solution

Inner perimeter=400 m.

Length (l)=90 m.

 Perimeter of two semicircles=4002×90=400180=220m

 Perimeter of one semicircle=2202=110 m

 Radius=Perimeterπ=11022×7=35 m

Width of the track=14 m

 Outer radius(R)=35+14=49 m and outer perimeter =2×90 m+2πr=180+2×227×49=180+154×2=180+308 m=488 m

and area of track =2×(90×14)+(πR2πr2)=2×1260+227(492352)m2=2520+227(49+35)(4935) m2=2520+227×84×14 m2=2520+3696 m2=6216 m2


Mathematics
RD Sharma
Standard VIII

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