Question

The ratio of the radius of circle is 4 is to 3 what is the ratio of their circumference

Answer 1

Question:

The ratio of the radii of two circles is 4:3 then what is the ratio of their circumferences.

Answer:

The required ratio of the circumferences of the two circles is , 4:3 .

Note:

• The diameter of a circle is double of its radius, ie; d = 2•r

• The circumference of the circle is ;

C = 2•π•r = π•d

• The area of the circle is;

A = π•r^2 = π•d^2/4

Solution:

Let the radius of the bigger circle be "r1" and the radius of the smaller circle be "r2" .

According to the question,

The ratio of radii of the two circles is 4:3 .

Thus,

=> r1:r2 = 4:3

=> r1/r2 = 4/3 ---------(1)

Now,

Let the circumference of the bigger circle be "C1" and the circumference of the smaller circle be "C2".

Thus,

C1 = 2•π•r1 ------(2)

C2 = 2•π•r2 --------(3)

Now,

Dividing eq-(2) by eq-(3), we get;

=> C1/C2 = 2•π•r1/2•π•r2

=> C1/C2 = r1/r2

=> C1/C2 = 4/3

=> C1:C2 = 4:3

Hence,

The required ratio of the circumferences of the two circles is , 4:3 .