A rectangle with dimensions \(8\) cm by \(15\) cm is inscribed in a circle. What is the number of centimeters in the circumference of the circle? Express your answer in terms of \(\pi\).

["Title: Circumference of the Circle for a Rectangle Inscribed in It | (8 , \ ext{cm} \ imes 15 , \ ext{cm})", "When a rectangle is inscribed in a circle, the diagonal of the rectangle becomes the diameter of the circle. Understanding this geometric relationship allows us to calculate the circumference efficiently. This article explores how to find the circumference of the circle when a rectangle with dimensions (8 , \ ext{cm}) by (15 , \ ext{cm}) is perfectly fitted inside it.", "### Understanding the Geometry", "A rectangle inscribed in a circle means all four corners touch the circle’s boundary. The diagonal of the rectangle passes through the center of the circle and equals the diameter.", "Given:\n- Rectangle width = (8 , \ ext{cm})\n- Rectangle length = (15 , \ ext{cm})", "### Step 1: Find the Diagonal Using the Pythagorean Theorem", "The diagonal (d) of the rectangle can be calculated using the Pythagorean theorem:", "[\nd = \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17 , \ ext{cm}\n]", "This diagonal is the diameter of the circle.", "### Step 2: Use the Diameter to Find the Circumference", "The circumference (C) of a circle is given by:", "[\nC = \pi \ imes d\n]", "Substitute (d = 17 , \ ext{cm}):", "[\nC = 17\pi , \ ext{cm}\n]", "### Conclusion", "The circle in which a rectangle measuring (8 , \ ext{cm}) by (15 , \ ext{cm}) is inscribed has a circumference of exactly (17\pi) centimeters.", "[\n\boxed{17\pi} \ ext{ cm}\n]"]