Question

the radius of mars is about half the radius of earth. guadalupe cuts out circles to represent earth a 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? 7 in. what is the radius of the circle guadalupe cuts out for mars? 3.5 in. 7 in. 12.25 in. 14 in.

Explanation:

Step1: Find the radius of Earth's circle

The area formula of a circle is \(A = \pi r^{2}\). Given \(A = 49\pi\) in.², substitute into the formula:
\(49\pi=\pi r^{2}\). Divide both sides by \(\pi\): \(r^{2}=49\). Take the square root: \(r = 7\) in. (since radius \(r>0\)).

Step2: Find the radius of Mars' circle

Given the radius of Mars is half the radius of Earth. If Earth's radius \(r_{E}=7\) in, then Mars' radius \(r_{M}=\frac{1}{2}r_{E}\).
Substitute \(r_{E} = 7\) in: \(r_{M}=\frac{1}{2}\times7 = 3.5\) in.

Answer:

For Earth: \(7\) in.
For Mars: \(3.5\) in.