The diameter of a circle is doubled. By what factor is the area changed?
A) √2
B) 2
C) 4
D) √4
E) 1

Question

Quizplus · Accepted Answer

The area of a circle is given by A=πr^2 or A=(πd^2)/4, where d is the diameter. When the diameter is doubled, the new diameter is 2d. Thus, the new area is:
Anew = π(2d)^2/4 = π(4d^2)/4 = πd^2 = 4πr^2
The new area is 4 times the original area. So, the area is changed by a factor of 4, which is option C.

The Diameter of a Circle Is Doubled