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A = 2\pi \times 4 + 2\pi \times 16
A = 8\pi + 32\pi
A = 40\pi
Thus, the surface area of the cylindrical shell is \(\boxed{40\pi}\) square centimeters.**Question:
A 5 cm by 12 cm rectangle is inscribed in a circle. What is the circumference of the circle in centimeters? Express your answer in terms of \(\pi\).
To find the circumference of the circle, we first need to determine the diameter of the circle. Since the rectangle is inscribed in the circle, the diagonal of the rectangle is the diameter of the circle. We can calculate the diagonal using the Pythagorean theorem:
The diameter of the circle is 13 cm. The circumference \(C\) of a circle is given by the formula:
C = \pi \times d
Substituting the diameter:
C = \pi \times 13 = 13\pi \text{ cm}