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 the formula for the area of a circle

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

Step2: Substitute the given area into the formula

Given \(A = 49\pi\) in.², substitute into \(A=\pi r^{2}\):
\(49\pi=\pi r^{2}\)

Step3: Solve for \(r^{2}\)

Divide both sides of the equation \(49\pi=\pi r^{2}\) by \(\pi\):
\(r^{2}=\frac{49\pi}{\pi}=49\)

Step4: Solve for \(r\)

Take the square root of both sides. Since \(r>0\) (radius is a non - negative quantity), \(r = \sqrt{49}=7\)

Answer:

7 in.