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प्रश्न
The inside perimeter of a running track shown in the figure is 400 m. The length of each of the straight portions is 90 m, and the ends are semicircles. If the track is 14 m wide everywhere, find the area of the track. Also, find the length of the outer boundary of the track.
उत्तर
Length of the inner curved portion (400 - 2 × 90) = 220 m
∴ Length of each inner curved path`=220/2=110 "m"`
Thus, we have:
⇒ πr = 110
`⇒ 22/7"r" = 110`
`=> "r" = (110xx7)/22`
⇒ r =35m
Inner radius = 35 m
Outer radius = (35 + 14) = 49 m
Area of track = {Area of the two rectangles [each(90 × 14)] + Area of the circular ring with R = 49 m and r = 35 m)}
`=(2xx90xx14)+22/7xx[(49)^2-(35)^2]`
`=2520 + 22/7xx(2401-1225)`
`= 2520 + 22/7xx1176`
= 2520 + 3696
= 6216 m2
Length of the outer boundary of the track
`=(2xx90+2xx22/7xx49)`
= 488 m
Therefore, the length of the outer boundary of the track is 488 m and the area of the track is 6216 sq. m.
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