High School

The circumference of a circle is [tex]22\pi[/tex] inches. What is the area, in square inches? Express your answer in terms of [tex]\pi[/tex].

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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