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Find the radius A=25π ft2A=25\pi\,\text{ft}^2

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Full solution

Q. Find the radius A=25π ft2A=25\pi\,\text{ft}^2
  1. Area Formula: To find the radius of a circle given its area, we use the formula for the area of a circle, which is A=πr2A = \pi r^2, where AA is the area and rr is the radius. We are given that A=25πA = 25\pi square feet.
  2. Set Up Equation: We set up the equation with the given area: 25π=πr225\pi = \pi r^2.
  3. Isolate Radius: To solve for rr, we divide both sides of the equation by π\pi to isolate r2r^2: 25ππ=r2\frac{25\pi}{\pi} = r^2.
  4. Simplify Equation: Simplifying the equation, we get 25=r225 = r^2, since π/π\pi/\pi equals 11.
  5. Find Radius: To find rr, we take the square root of both sides of the equation: 25=r\sqrt{25} = r.
  6. Find Radius: To find rr, we take the square root of both sides of the equation: 25=r\sqrt{25} = r. The square root of 2525 is 55, so r=5r = 5 feet.

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