Question

The inside perimeter of a practice running track with semi circular ends and straight parallel sides is 312 M. The length of the straight portions of the track is 90m .If the track has a uniform width of 2 metre throughout, find its area . Use the fig. 17.20.

Answer 1

Answer:

Track area = 636.46 cm²

Step-by-step explanation:

The inside perimeter of a practice running track with semi circular ends and straight parallel sides is 312 m.

The length of the straight portions of the track is 90 m.

Let the inner radius of circular track be x m.

Inside perimeter = Circumference of two semi-track + Two straight track

                           $=2\pi x+90+90$

                           $312=180+2\pi x$

                           $x=21\ m$

Inner radius = 21 m

Width of track = 2 m

Outer radius = 23 m

Track area = Outer Area - Inner Area

                   $=(\pi \cdot 23^2+90\times 46)-(\pi \cdot 21^2+90\times 42)$

Track area = 636.46 cm²

Answer 2

The length of the straight portion of the track is 90 m.and

The inside perimeter 312m

∴πr+length+πr+length=312

⇒πr+90+πr+90=312

⇒2πr=312−180

⇒2πr=132

⇒r=

2π

132

⇒r=

2×22

132×7

⇒r=

44

924

⇒r=21

Width of the running track =2m

∴ Radius of outer perimeter=21+2=23

∴ Area of outer perimeter =

2

π(23)

2

+(90×23×2)+

2

π(23)

2

=

7×2

22(23)

2

+(90×23×2)+

7×2

22(23)

2

=831.285+4140+831.285=5802.57

∴ Area of inner perimeter =

2

π(21)

2

+(90×21×2)+

2

π(21)

2

=

7×2

22(21)

2

+(90×21×2)+

7×2

22(21)

2

=693+3780+693=5166

Area of the track= Area of outer perimeter − Area of inner perimeter

=5802.57−5166 =636.57m

2