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 semi-circles. If the track is 14 m wide every where, find the area of the track. Also, find the length of the outer boundary of the track.



Asked by Topperlearning User | 27th Jul, 2017, 02:33: PM

Expert Answer:

begin mathsize 12px style Length space of space the space curved space portion space equals open parentheses 400 space minus space 2 space cross times space 90 close parentheses space equals space 220 space straight m
therefore space Length space of space the space inner space curved space part space equals space 110 space straight m
Let space the space radius space of space the space inner space curved space part space be space straight r.
Then comma space πr space equals space 110 space straight m
rightwards double arrow space 22 over 7 straight r space equals space 110 space straight m space rightwards double arrow space straight r space equals space 110 space cross times space 7 over 22 space equals space 35 space straight m
therefore space inner space radius space equals space 35 space straight m
outer space radius space equals space 35 space plus space 14 space equals space 49 space straight m
therefore space area space of space the space track space equals space open parentheses area space of space 2 space rectangles space each space 90 straight m space cross times space 14 straight m close parentheses space plus space open parentheses area space of space circular space ring space with space straight R space equals space 49 space straight m comma space straight r space equals space 35 straight m close parentheses
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space open curly brackets open parentheses 2 space cross times space 90 space cross times space 14 close parentheses space plus space straight pi space open parentheses straight R squared minus space straight r squared close parentheses close curly brackets space straight m squared
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space open curly brackets 2520 space plus 22 over 7 open parentheses 49 squared space minus space 35 squared close parentheses close curly brackets space straight m squared
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space open curly brackets 2520 space plus space 22 over 7 open parentheses 49 space plus space 35 close parentheses open parentheses 49 space minus space 35 close parentheses close curly brackets space straight m squared
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space open curly brackets 2520 space plus space 3696 close curly brackets space equals space 6216 space straight m squared
therefore space area space of space the space track space equals space 6216 space straight m squared
Length space of space the space boundary space of space the space track space equals space open parentheses 2 space cross times space 90 space plus space 2 space cross times space 22 over 7 space cross times space 49 close parentheses space equals space 488 space straight m
Hence comma space area space of space the space track space equals space 6216 space straight m squared comma space outer space perimeter space of space the space track space equals space 488 space straight m end style

Answered by  | 27th Jul, 2017, 04:33: PM

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