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 - Mathematics

Sum

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

Length of the inner curved portion (400 - 2 × 90) = 220 m

∴ Length of each inner curved path=220/2=110  "m"

Thus, we have:

⇒ πr = 110

⇒ 22/7"r" = 110

=> "r" = (110xx7)/22

⇒ r =35m

Outer radius = (35 + 14) = 49 m
Area of track = {Area of the two rectangles [each(90 × 14)] + Area of the circular ring with R = 49 m and r = 35 m)}

=(2xx90xx14)+22/7xx[(49)^2-(35)^2]

=2520 + 22/7xx(2401-1225)

= 2520 + 22/7xx1176

= 2520 + 3696

= 6216 m

​Length of the outer boundary of the track

=(2xx90+2xx22/7xx49)

= 488 m

Therefore, the length of the outer boundary of the track is 488 m and the area of the track is 6216 sq. m.

Is there an error in this question or solution?

APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 18 Area of Circle, Sector and Segment
Exercise 18B | Q 60 | Page 836