Question

a race track is in the form of a ring whose river circumference is 40π m and outer circumference is 50π m. find the width of track​

Answer 1

Answer:

Hint: The concept here to be used is to find radius of both inner track and outer track and when we get r1

andr2

then from the diagram we can see that width is equal to difference in the radius of both tracks (r1−r2)

when r1>r2

Complete step by step solution:

Also formula for circumference=2πr

⇒

Inner circumference of track =352

m

Let us assume radius to be r2

2πr2=352m

……. 1

⇒

Outer circumference of race track =396m

Let us assume radius to be r1

2πr1=396m

Solving 1 and 2

r2=3522π

r1=3962π

Now width of track is

⇒r1−r2 {∵r1>r2}

⇒3962π−3522π

⇒396−3522π

⇒442π

⇒7.00282

So the width of the track is 7.00282 m.

Note: You can also find the width from finding the diameters of respective tracks rather than finding radius of the tracks

Then the formula of width ⇒d1−d22

Where d1

and d2

are respective track diameters.