Question

The inside perimeter of a running track (shown) is 400 m. The length of each of the straight portion is 90 m and the ends are semi-circles. If the track is everywhere 14 m wide, find the area of the track. Also, find the length of the outer running track.

Answer 1

The inside perimeter of the track $=400m$

Width of the track $=14m$

The total length of the two straight portions $=90+90=180m$

Therefore, the length of the remaining portion (Semi-circular portions) $=400-180=220m$

Circumference of the two remaining semi-circular portions $=\pi r+\pi r=2\pi r$

${}^{\prime }{r}^{\prime }$ is the radius.

$\Rightarrow 2\pi r=220$

$\Rightarrow 2\times \frac{22}{7}\times r=220$

$\Rightarrow 44r=220\times 7$

$\Rightarrow r=35m$

So, the radius of the circular portion of the outer running running track $=35m+14m=49m$

Area of the track $=$ [Area of the two rectangles of dimensions $90m\times 14m$] + The area of the circular rings. [Two semi- circular rings will make a circle]

$=2\times 90\times 14+\frac{22}{7}\times ({49}^2-{35}^2)$

$=2520+\frac{22}{7}\times (2401-1225)$

$=2520+\frac{22}{7}\times (2401-1225)$

$=2520+\frac{22\times 1176}{7}$

$=6216m^2$

Length of the outer running track $=2\times$ length of straight track (i.e. $90m$) $+2\times$ Circumference of outer circle

$=2\times 90+2\times \frac{22}{7}\times 49$

$=180+308=488m$

Length of the outer running track $=488m$