If the radius of a circle is doubled, by what factor does the circumference increase?
2π(2r) / 2πr = 2
To find the factor by which the circumference increases when the radius of a circle is doubled, we first need to understand the relationship between the circumference and the radius of a circle.
The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. This formula tells us that the circumference is directly proportional to the radius.
When the radius is doubled, the new radius becomes 2r. Plugging this new value into the formula, we get:
C = 2π(2r)
C = 4πr
Comparing this to the original formula, we can see that the new circumference is 4 times the original circumference, given that the radius is doubled. Therefore, the factor by which the circumference increases is 4, or the new circumference is 4 times the original circumference.