A racetrack is in the form of a ring whose inner circumference is 352 m and outer circumference is 396 m. Find the width and the area of the track.

Consider the race track as shown below,

The inner and outer radius of track is ‘r’ cm and ‘R’ cm respectively.

Let inner and outer circumference be ‘C_{1}’ and C_{2}’ respectively.

C_{1} = 352 m and C_{2} = 396 m.

We know,

Circumference of circle = 2πr

Where r = radius of the circle

C_{1} = 2πr and C_{2} = 2πR

⇒ 2πr = 352 and 2πR = 396

On rearranging,

⇒ r = 56 m and R = 63 m

So, the width of the race track = R – r,

⇒ Width of the race track = 63 – 56

⇒ Width of the race track = 7 m

Area of race track = area of outer circle – area of inner circle

⇒ Area of track = πR^{2} – πr^{2} (put values of r and R)

⇒ Area of track = π(63^{2}) – π(56^{2})

⇒ Area of track = π(63^{2} – 56^{2}) (taking π common from R.H.S)

⇒ Area of track = π(3969 – 3136)

⇒ Area of track = π×833

= 22×119

= 2618 m^{2}

The width of tack is 7 m and area of track is 2618 m^{2}.

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