what is the area of a circle with a circumference of 22 pi in.? expressed in pi in. squared? and what are the steps to arrive at the solution?
Circle circumference = 2 pi r = 22 pi
Solve for r by dividing both sides by 2 pi, then put value in area equation.
Circle area = pi r^2
Answer is 22. Pi plus radius = circumf mace
To find the area of a circle with a given circumference, you can use the following formula:
Circumference = 2 * π * radius
In this case, the circumference is given as 22π inches. Considering that the formula above gives the circumference as 2π times the radius, we can set up an equation to solve for the radius.
22π = 2 * π * radius
To solve for the radius, divide both sides of the equation by 2π:
radius = (22π) / (2π)
radius = 11 inches
Now that we have the radius, we can find the area of the circle using the formula:
Area = π * radius^2
Substituting the value of the radius we just found:
Area = π * (11 inches)^2
Simplifying:
Area = π * 121 square inches
Thus, the area of a circle with a circumference of 22π inches is 121π square inches.
To find the area of a circle with a given circumference, you need to use the formula:
A = (C^2) / (4π)
where A represents the area and C represents the circumference.
Step 1: Given the circumference of 22π inches, substitute this value into the formula:
A = ((22π)^2) / (4π)
Step 2: Simplify the equation by squaring the value in parentheses:
A = (484π^2) / (4π)
Step 3: Cancel out the common factor of π in the numerator and the denominator:
A = (484π) / 4
Step 4: Simplify the expression further by dividing the numerator by the denominator:
A = 121π
Therefore, the area of the circle with a circumference of 22π inches is 121π square inches.