1.

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

Answer» Length of the interior curved protion `= (400 - 2 xx 90) m = 220 m`
Each curved part = 110 m
`pi r = 110`
`r = (110)/(pi) = (110 xx 7)/(22) m = 35 m`
`:.` Inner radius = 35 m
`:.` Outer radius `= (35 + 14) m = 49 m`
`:.` Area of the track `= 2 xx` Area of rectangles each of `90 m xx 14 m` + Area of (circular ring with `r_(1) = 49 m and r_(2) = 35 m`)
`= 2(90 xx 14) + (22)/(7) xx [(49)^(2) - (35)^(2)]`
`= 2520 m^(2) + (22)/(7) (49 + 35) (49 - 35) m^(2)`
`= 2520 m^(2) + (22 xx 84 xx 14)/(7) m^(2)`
`= 2520 m^(2) + 3694 m^(2) = 6216 m^(2)`
Length of outer track `= (2 xx 90 + 2 xx (22)/(7) xx 49) m`
`180 m + 308 m = 488 m`


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