Question

The ratio of the outer and inner circumference of a circular path is 23:22 . if the path is 5 m wide then the find the diameter of the inner circle .

Answer 1

Let R and r be the outer and inner radii of the circular path.( now see pic)

Let R = 23x and r = 22x

It is given that the width of the path is 5 m wide

∴ R – r = 5 m

⇒ 23x – 22x = 5 m

⇒ x = 5 m

Thus, the external diameter of the circular road = 2 × 23 × 5 m = 230 m and the internal diameter of the circular road = 2 × 22 × 5 m = 220 m

Answer 2

Answer:

220 m is the inner diameter of the circle.

Step-by-step explanation:

Given:-

The ratio of the outer and the inner circumference of a circular path is 23:22.

The path is 5 m wide.

To find:-

The diameter of the inner circle.

Let the radius of the outer circle be R.

And the radius of the inner circle is r.

Also, assume the common ratio be $x$.

Since the ratio of the outer and the inner circumference of a circular path is 23:22, i.e.,

The ratio of the outer and the inner circumference of a circular path = $\frac{23x}{22x}$

⇒ $\frac{2\pi R}{2\pi r}=\frac{23x}{22x}$

⇒ $\frac{R}{r}=\frac{23x}{22x}$

⇒ $R=23x$ and $r=22x$

It is also given that the difference between the outer radius and the inner is 5 m.

⇒ R - r = 5 m

⇒ 23x - 22x = 5

⇒ x = 5 m

Now, the inner radius of the circle = 22x

                                                          = 22(5)

                                                          = 110 m

So, the diameter of the inner circle = 2 × 110

                                                           = 220 m

Therefore, 220 m is the inner diameter of the circle.

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