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Question

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.


Solution

vidya

Let the radius of the inner semi-circular ends = m. 

Inner perimeter of the track = 400 m

 90 + πr + 90 + πr = 400 (Circumference of the semi-circle = πr)

2πr = 220 m

 r = 35 m

 Area of the track = Area of the ring AEHD + Area of rectangle ABFE + Area of ring BFGC + Area of rectangle CDHG

= 12× π × (492352)+90 × 14 + 12× π × (492352)+90 × 14
= π × (240112285)+2(90 × 14)
= 227× (1176)+2(1260)

= 3696 + 2520

= 6216 sq. m.

Length of the outer running track = EF + Length of arc FG + GH + Length is arc HE

= 90 + [π × (35 + 14)] + 90 + [ π × (35 + 14)]

= [2π × 49] + 180

227× 2 (49)+180

= 308 + 180

= 488 m


Mathematics
Secondary School Mathematics X
Standard X

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