Question

The inside perimeter of a running track (shown in Fig.) 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 1

Inner perimeter=400 m.

Length (l)=90 m.

$\therefore Perimeteroftwosemicircles=400-2\times 90=400-180=220m$

$\therefore Perimeterofonesemicircle=\frac{220}{2}=110m$

$\therefore Radius=\frac{Perimeter}{\pi }=\frac{110}{22}\times 7=35m$

Width of the track=14 m

$\therefore Outerradius\left(R\right)=35+14=49mandouterperimeter=2\times 90m+2\pi r=180+2\times \frac{22}{7}\times 49=180+154\times 2=180+308m=488m$

and area of track $=2\times (90\times 14)+(\pi R^2-\pi r^2)=2\times 1260+\frac{22}{7}({49}^2-{35}^2)m^2=2520+\frac{22}{7}(49+35)(49-35)m^2=2520+\frac{22}{7}\times 84\times 14m^2=2520+3696m^2=6216m^2$