# The equation r = (sqrt A)/(pi) gives the radius r of circle with area A. What is the radius of a circle with the given area? Write your answer as a simplified radical and as a decimal rounded to the nearest hundredth.

a. 50 ft^2

pi r^2 = A

r^2 = (A/pi)

r = sqrt (A/pi)
which is
sqrt A/sqrt pi

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## r = sqrt(50) /sqrt pi = sqrt (25*2) /sqrt pi

= (5 sqrt 2) /sqrt pi

3.98 ft

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## It is incorrect then

The area of a circle is pi r^2

a = pi r^2
r^2 = a/pi
r = sqrt (a/pi) = sqrt a/srt pi
NOT
(sqrt a) / pi NO !

The text did NOT make that error, like no way. It is in your parentheses.

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## To find the radius of a circle with a given area, we can use the equation r = sqrt(A) / pi. In this case, the given area A is 50 ft^2.

To find the radius, we need to substitute the value of A into the equation and simplify:

r = sqrt(50) / pi

sqrt(50) = sqrt(25 * 2) = sqrt(25) * sqrt(2) = 5 * sqrt(2)

Substituting back into the equation:

r = (5 * sqrt(2)) / pi

Now, let's calculate the decimal approximation rounded to the nearest hundredth.

Using the approximation value of pi as 3.14, we can calculate:

r ≈ (5 * sqrt(2)) / 3.14 ≈ 7.97 ft (rounded to the nearest hundredth)

Therefore, the radius of a circle with an area of 50 ft^2 is approximately 5 * sqrt(2) or 7.97 ft.