Question

If the area of a ˚le is quadrupled, what is the ratio of the ˚le's new ˚umference to its old ˚umference?

a) 2:1
b) 1:2
c) 1:4
d) 4:1

Answer 1

When the area of a circle is quadrupled, the new circumference is double the old circumference, leading to a ratio of 2:1.

Step-by-step explanation:

If the area of a circle is quadrupled, the new area is four times the old area. To find the ratio of the new circumference to the old circumference, we need to understand the relationship between the area and the circumference of a circle. The area A of a circle is given by the formula A = πr^2, where r is the radius, and the circumference C is given by C = 2πr. If the area is quadrupled, then the new area A' is A' = 4πr^2, which suggests that the new radius r' is double the old radius (since A' = π(r')^2 and r' = 2r). Thus, the new circumference C', which is C' = 2πr' will be double the old circumference C, because C' = 2π(2r) = 2(2πr) = 2C.

Therefore, the ratio of the new circumference to the old circumference is 2:1.