The ratio of the perimeters of two circles is $1 : 3$ . Draw two concentric circles where the diameter of the inner circle is $4$ cm. The difference between the radii of the two concentric circles is

Open in App

Solution

Perimeter of a circle = $2 π r$ [where r is the radius of a circle]

Given perimeters' ratio is 1 : 3

Therefore

$\frac{p_{1}}{p_{2}} = \frac{2 π r_{1}}{2 π r_{2}} = \frac{1}{3}$

So, $\frac{r_{1}}{r_{2}} = \frac{1}{3}$

Diameter of inner circle = 4cm

Therefore radius will be 2cm

$r_{1} = 2 c m$

$\frac{2}{r_{2}} = \frac{1}{3}$

$r_{2} = 6 c m$

Difference between the radii of two concentric circles is $r_{2} - r_{1} = 6 - 2 = 4 c m$

Suggest Corrections

Similar questions

Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on the outer circle, construct the pair of tangents to the inner circle.

Two concentric circles are of radii 13 cm and 5 cm. Find the length of the chord of the outer circle which touches the inner circle.

13 c m

5 c m

12

72

π = 3

Join BYJU'S Learning Program