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.
Let the radius of the inner semi-circular ends = r 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 × (492−352)+90 × 14 + 12× π × (492−352)+90 × 14
= π × (2401−12285)+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