we know that
Area of a circle is equal to
[tex] A=\pi r^{2} [/tex]
where
r is the radius of the circle
Step [tex] 1 [/tex]
Find the radius of the circle for an area equal to [tex] 135cm^{2} [/tex]
[tex] 135=\pi r^{2} \\\\ r= \sqrt{\frac{135}{3.14}} \\ \\ r=6.56 cm [/tex]
Step [tex] 2 [/tex]
Find the radius of the circle for an area equal to [tex] 155cm^{2} [/tex]
[tex] 155=\pi r^{2} \\\\ r= \sqrt{\frac{155}{3.14}} \\ \\ r=7.03 cm [/tex]
[tex] 6.56\ cm \leq r \leq 7.03\ cm [/tex]
One solution for this problem could be
[tex] r=7\ cms [/tex]
because
[tex] 6.56\ cm \leq 7\ cm \leq 7.03\ cm [/tex]
and
[tex] A=\pi *7^{2} =153.86cm^{2} [/tex]
[tex] 135\ cm^{2} \leq 153.86\ cm^{2} \leq 155\ cm^{2} [/tex]
therefore
the answer is
The radius of the circle must be
[tex] 6.56\ cm \leq r \leq 7.03\ cm [/tex]
We will see that she can use any circle with a radius that is a solution of the inequality:
6.6 cm < R < 7 cm
We know that the area of a circle of radius R is given by:
So we want to have an area between 135 cm^2 and 155cm2, so we have:
135 cm^2 < A < 155 cm^2
135 cm^2 < 3.14*R^2 < 155 cm^2
Now we can solve that inequality for R, first we divide the 3 parts by 3.14
(135 cm^2)/3.14 < R^2 < (155cm^2)/3.14
43 cm^2 < R^2 < 49.4 cm^2
Now we take the square root to get:
√(43 cm^2 ) < R < √(49.4 cm^2 )
6.6 cm < R < 7 cm
Then any circle with a radius between 6.6cm and 7cm can be used.
If you want to learn more about circles, you can read:
https://brainly.com/question/14283575
