Final answer:
To find the diameter of a circle with an area of 169π square inches, solve for the radius by dividing the area by π and taking the square root. The diameter is twice the radius, resulting in a diameter of 26 inches.
Step-by-step explanation:
The student is asking to identify the diameter of a circle given that the area (A) is 169π square inches. The formula for the area of a circle is A = πr². To find the diameter, we need to solve for the radius first and then double it, because the diameter (D) is equal to 2 times the radius (2r).
First, we substitute the given area into the area formula:
169π = πr². We can divide both sides by π to get 169 = r². Taking the square root of both sides gives us r = 13. Therefore, the diameter D is 2r, which equals 2 × 13, or 26 inches.