Answer:
[tex]\boxed{\textsf{ The ratio of the circumference of two circles is \textbf{ 4:7}.}}[/tex]
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 ,
[tex]\qquad\boxed{\boxed{\sf Circumference_{(circle)}= 2\pi r }}[/tex]
Now let the circumference of the first circle be [tex]\sf C_1 [/tex] and the circumference of the second circle be [tex]\sf C_2 [/tex] .
Finding the ratios :-
[tex]\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}}}[/tex]
Hence the ratio of the circumferences is same as that of the radius .
