Answer :
Answer:
A = 121π in²
Step-by-step explanation:
The circumference (C) of a circle is
C = 2πr ( r is the radius )
Here C = 22π , that is
2πr = 22π ( divide both sides by 2π )
r = [tex]\frac{22\pi }{2\pi }[/tex] = 11
The area (A) of a circle is
A = πr² = π × 11² = 121π in²
Final answer:
The area of a circle with a circumference of 22π inches is 121π square inches.
Explanation:
The circumference of a circle is calculated using the formula C = 2πr, where r is the radius of the circle. When the given circumference is 22π inches, we can set up the equation 2πr = 22π, and solving for r, we get the radius r = 11 inches.
Now, to calculate the area of a circle, we use the formula A = πr². Substituting radius (r) = 11 inches into the formula, we find the area equals π * (11^2) = 121π square inches.
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