Question

THE INNER CIRCUMFERENCE OF A CIRCULAR TRACK IS 242M.THE TRACK IS UNIFORMLY 7M WIDE.FIND THE AREA OF THE TRACK

Answer 1

Inner Circumference = 242 m

=> 2 pi r = 242

=> 2 × 22 × r / 7 = 242

=> r = 242 × 7 / 44

=> r = 11 × 7 / 2

=> r = 77/2

=> r = 38.5 m

Inner Radius = 38.5 m

Outer Radius = Inner Radius + Width of track

Outer Radius = 38.5 + 7 = 45.5 m


Area of track = Outer Area - Inner Area

= pi R^2 - pi r^2

= pi ( R^2 - r^2)

= pi ( R +r) (R - r)

= pi × 84 × 7

= 22 × 84 × 7 / 7

= 22 × 84

= 1848 m^2

Answer 2

hiii!!!

here's ur answer...

given the inner circumference of the circular track is 242m.

therefore 2πr = 242m

==> 2 × 22/7 × r = 242m

==> 44/7 × r = 242m

==> r = 242/1 × 7/44

==> r = 5.5 × 7

==> r = 38.5m

VERIFICATION :-

inner circumference of the track = 2πr

= 2 × 22/7 × 38.5

= 1694/7

= 242m

hence verified

thus the radius of the inner circumference of the track is 38.5m.

GIVEN, that the track is 7m wide.

therefore radius of along with the track = 38.5 + 7

= 45.5m

area along with the track = πr²

= 22/7 × 45.5 × 45.5

= 45545.5/7

= 6506.5m²

area without track = πr²

= 22/7 × 38.5 × 38.5

= 32609.5/7

= 4658.5m²

therefore area of the track = 6506.5 - 4558.5

= 1848m²

hope this helps..!!