The area of a circle with radius r is given by the formula A=πr^2. If a circle has area 36π square inches, what is the radius?
πr^2 = 36π , divided each side by π
r^2 = 36
r = √36 = 6
To find the radius of the circle given its area, follow these steps:
Step 1: Recall the formula for the area of a circle: A = πr^2.
Step 2: Substitute the given area into the formula: 36π = πr^2.
Step 3: Divide both sides of the equation by π: (36π)/π = (πr^2)/π.
Step 4: Simplify the equation: 36 = r^2.
Step 5: Take the square root of both sides of the equation: √36 = √(r^2).
Step 6: Simplify the equation: 6 = r.
Therefore, the radius of the circle is 6 inches.
To find the radius of a circle, given its area, you can use the formula A = πr^2. In this case, the area is given as 36π square inches.
Step 1: Equate the given area to the formula: 36π = πr^2.
Step 2: Divide both sides of the equation by π to isolate the term r^2: 36π/π = πr^2/π.
Step 3: Cancel out π on the right side of the equation: 36 = r^2.
Step 4: Take the square root of both sides of the equation to solve for r: √(36) = √(r^2).
Step 5: Simplify the square root of 36, which gives two possible outcomes: r = 6 or r = -6.
Since we are dealing with a physical measurement, the radius cannot be negative. Therefore, the radius of the circle is 6 inches.