College

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 :

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.