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Answer :
Final answer:
Given the circumference of 22π inches, the radius is found to be 11 inches. Using the formula for the area of a circle, A = πr², the area is calculated as 121π square inches.
Explanation:
The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. Given that the circumference is 22π inches, we can determine the radius by dividing the circumference by 2π.
So, r = ½(22π) / π = 11 inches
Now that we have the radius, we can find the area of the circle using the formula A = πr². Therefore, the area A will be:
A = π(11 inches)² = π(121 inches²)
= 121π square inches.
This calculation is straightforward and does not require a calculator for exact values expressed in terms of π. However, if you wanted to express the answer as a decimal, you would then involve more complex calculations and consider the number of significant figures.
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