Question

a classmate states that if the radius of a circle is doubled, then its area is doubled. do you agree or disagree? if you disagree, how much greater do you think the area will be? select the answer from the drop - down lists to correctly complete the response. show hints. when the radius is squared, the area drop - down 1 the factor it is great. it will be drop - down 2 times as large (since ( a=pi r^{2} ), if ( r ) becomes ( 2r ), then ( a=pi(2r)^{2}=4pi r^{2} ))

Explanation:

Step1: Recall circle area formula

The area of a circle is $A = \pi r^2$, where $r$ is the radius.

Step2: Calculate area with doubled radius

Let new radius $r' = 2r$. New area $A' = \pi (2r)^2 = 4\pi r^2$.

Step3: Compare new and original area

$\frac{A'}{A} = \frac{4\pi r^2}{\pi r^2} = 4$

Answer:

Disagree. When the radius is squared, the area will not be twice as great. It will be 4 times as large since $\pi(2r)^2 = \pi(4r^2) = 4(\pi r^2)$.