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

Answer:

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

Step-by-step 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 :-

$\sf\implies C_1:C_2 = 2\pi r_1 : 2\pi r_2\\\\\sf\implies \dfrac{C_1}{C_2}= \dfrac{2\pi r_1}{2\pi r_2}\\\\\sf\implies \dfrac{C_1}{C_2}= \dfrac{2\pi }{2\pi } \times \dfrac{r_1}{r_2}\\\\\sf\implies \dfrac{C_1}{C_2}= \dfrac{4}{7} \\\\\sf:\implies \boxed{\pink{\frak{ C_1:C_2= 4:7}}}$

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