Q. 53.9( 24 Votes )

The inside perimeter of a running track (shown in Fig. 20.24) 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.


Answer :

Perimeter of the inner track = 2× Length of rectangle + perimeter of two semi-circular ends


Perimeter of the inner track = length + length + 2πr





Hence, the radius of inner circle = 35 m


Radius of outer track = radius of inner track + width of the track


Radius of outer track = 35 + 14 = 49m


Length of outer track = 2× Length of rectangle + perimeter of two outer semi-circular ends


Length of outer track = 2× 90 + 2πr


Length of outer track =


Length of outer track =


Area of inner track = area of inner rectangle + area of two inner semi-circles


Area of inner track = length× breadth + πr2


Area of inner track =


Area of inner track = 6300 + 3850


Area of inner track = 10150 m2


Area of outer track = area of outer rectangle + area of two outer semi-circles


Breadth of outer track = 35 + 35 +14 + 14 = 98 m


Area of outer track = length× breadth + πr2


Area of outer track =


Area of outer track = 8820 + 7546


Area of outer track = 16366 m2


Area of path = area of outer track – area of inner track


Area of path = 16366 – 10150 = 6216 m2


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