The circumference of the bigger circle is 56.
Step-by-step explanation:
Step 1:
The circumference of a circle is given by twice the product of π and its radius r.
The circumference of a circle = [tex]2\pi r.[/tex]
The scale factor is 4: 7, so the circumference too will be of ratio 4: 7.
Step 2:
We equate the ratios to each other to find the value of circumference for the bigger circle.
4: 7 is equal to 32: x, assume x is the circumference of the bigger circle.
We divide the ratios as such;
[tex]\frac{4}{32} = \frac{7}{x}, x = 7 (\frac{32}{4} ) = 56.[/tex]
So the circumference of the bigger circle is 56.
