The inside perimetre of a running track is 400m The length of each of the straight portion is 90m - Maths - Areas Related to Circles

Question

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

Lalit Mehra · Accepted Answer

Dear Student!

Let the radius of the inner semi-circular ends be r m Given, Inner perimeter of running track = 400 m Circumference of the semi-circle, BC and AD = $π r$ âˆ´

$\Rightarrow 90 m + π r + 90 m + π r = 400 m \Rightarrow 2 π r = 400 m - 180 m = 220 m \Rightarrow 2 \times \frac{22}{7} \times r = 220 m \Rightarrow r = \frac{220 \times 7}{22 \times 2} m = 35 m$ Area of the track = Area of the ring AEHD + Area of rectangle ABFE + Area of ring BFGC + Area of rectangle CDHG $= \frac{1}{2} π [(35 + 14)^{2} - (35)^{2}] m^{2} + 90 m \times 14 m + \frac{1}{2} π [(35 + 14)^{2} - (35)^{2}] m^{2} + 90 m \times 14 m$ $= π [(49)^{2} - (35)^{2}] m^{2} + 2 \times 90 m \times 14 m$ $= \frac{22}{7} \times 1176 m^{2} + 2520 m^{2}$ = 3696 m2 + 2520 m2 = 6216 m2 âˆ´ The area of the track is 6216 m2 Length of the outer running track = EF + Length of arc, FG + GH + Length is arc, HE $= 90 m + π \times (35 + 14) m + 90 m + π \times (35 + 14) m$ $= 180 m + 2 \times \frac{22}{7} \times 49 m$ = 180m + 308m = 488m âˆ´ The length of the outer running track is 488 m Cheers!

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