Question

the radius of mars is about half the radius of earth. guadalupe cuts out circles to represent earth and mars in a diagram. she cuts out a circle with an area of 49π in.² to represent earth. what is the radius of the circle guadalupe cuts out for earth? 3.5 in, 7 in, 14 in, 24.5 in.

Explanation:

Step1: Recall circle - area formula

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

Step2: Substitute given area

We are given that $A = 49\pi$ in². Substituting into the formula $49\pi=\pi r^{2}$.

Step3: Solve for $r$

Divide both sides of the equation $49\pi=\pi r^{2}$ by $\pi$. We get $49 = r^{2}$. Taking the square - root of both sides, since $r>0$ (radius is a non - negative quantity), $r = 7$ in.

Answer:

7 in.