Question

A circle has a radius of 3 feet. A bigger circle is created so that has a ratio of radii is 4:7 with the smaller circle. What is the ratio of the circumferences? *

Answer 1

`\boxed{\textsf{ The ratio of the circumference of two circles is \textbf{ 4:7}.}}`

Explanation:

Given that the circle has a radius of 3 feet . And a bigger circle is created so that the ratio of radii of the two circles is 4 : 7 . And we need to find the ratio of the circumferences .

Now we know that the circumference of the circle is given by ,

`\qquad\boxed{\boxed{\sf Circumference_((circle))= 2\pi r }}`

Now let the circumference of the first circle be
`\sf C_1` and the circumference of the second circle be
`\sf C_2` .

Finding the ratios :-

`\sf\implies C_1:C_2 = 2\pi r_1 : 2\pi r_2\\\\\sf\implies (C_1)/(C_2)= (2\pi r_1)/(2\pi r_2)\\\\\sf\implies (C_1)/(C_2)= (2\pi )/(2\pi ) * (r_1)/(r_2)\\\\\sf\implies (C_1)/(C_2)= (4)/(7) \\\\\sf:\implies \boxed{\pink{\frak{ C_1:C_2= 4:7}}}`

Hence the ratio of the circumferences is same as that of the radius .