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A small decorative table has a diameter of 50 cm and a height of 66 cm. Its table cover hangs down to the floor on all sides. What is the area of the cover?

Circular table cover

I modelled the table as an open cylinder, so the area would be $\pi r^2 + 2 \pi r h = \pi \times 25^2 + 2 \pi \times 25 \times 66 = 12,330.75$ cm$^2$.

However, another approach used was that the diameter of the entire circular table cover is 50 + 66 + 66 = 182 cm. (The cover becomes a circle when spread out and opened completely.) So, the area is $\pi (d/2)^2 = \pi \times (182/2)^2 = 26,015.53$ cm$^2$.

Both these approaches seem logical to me, but what is the correct answer?

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    The second. In the first one you're estimating way below the actual area. Comparatively the first approach is like estimating the length of the curve $\{(t,\sin(t)):0$\{(0,0)\}$ to $\{(0,2\pi)\}$ ($=2\pi$). – 2017-01-19
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    `an open cylinder` The area of an open cylinder doesn't count the "folds" which a round table cloth necessarily makes on the side. The correct answer is the second one. – 2017-01-19

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