Question

The ratio of the radii of two wheels is 4 : 5. Find the ratio of their circumference.

Answer 1

Given:-

→Ratio of radii of two wheels = 4:5

To find:-

→Ratio of their circumference

Solution:-

Let the radius of the first wheel be r₁ and the radius of the second whell be r₂.

• Circumference of a circle = 2πr

Now let:-

=> r₁ = 4x

=> r₂ = 5x

Circumference of the 1st wheel :-

= 2πr₁

= 2π4x

= 8πx

Circumference of the 2nd wheel:-

= 2πr₂

= 2π5x

= 10πx

Now, ratio of their circumference:-

= 8πx/10πx

= 8/10

= 4/5

= 4:5

Thus, ratio of circumference of the wheels is 4:5.

Some Extra Information:-

Circle : A circle is all points in the same plane that lie at an equal distance from a centre point.

• Circumference of a circle = 2πr

• Area of a circle = πr²

• Diameter of a circle = 2r

Answer 2

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What is the ratio of the circumference of two circles if the ratio of their radii is 4:5..??

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Let the rational between radii of two wheels be x.

Hence, the radii of two wheels will be 4x and 5x.

The ratio between radii of two wheels will be

$\bold{ \frac{4x}{5x} \: \: or \: \: \: \frac{4}{5} }$

We know the circumference of circle or wheel is 2πr ..where r is the radius of the wheel.

The circumference of first wheel = 2πr1

The circumference of second wheel = 2πr2

The ratio between circumferences

2πr1 / 2πr2

= r1 / r2

$\bold{\frac{2\pi \: r1}{2\pi \: r2} } \bold{= \frac{r1}{r2} }$

As above we have derived ratio of radii if two wheel as 4/5...Hence,

$\bold{\frac{r1}{r2} = \frac{4}{5} }$

Thus ratio between the circumferences of two wheels is 4/5

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The ratio between the circumferences of two wheels is 4:5