The volume of a cylinder is \(500\pi\) and the radius is 5 cm. The height of the cylinder is equal to the diagonal of a square. Find the perimeter of the square.

40\sqrt{2} cm
40 cm
10\sqrt{2} cm
80\sqrt{2} cm

Correct answer: 40\sqrt{2} cm

Solution

Using \(V=\pi r^2 h\), we get \(500\pi = \pi \times 5^2 \times h\), so \(h=20\) cm. This height is the diagonal of the square, so side \(= 20/\sqrt{2} = 10\sqrt{2}\) cm, and perimeter \(= 4 \times 10\sqrt{2} = 40\sqrt{2}\) cm.

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