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Seven identical cylindrical chalk-sticks are fitted tightly in a cylindrical container. The figure below shows the arrangement of the chalk-sticks inside the cylinder. The length of the container is equal to the length of the chalk-sticks. The ratio of the occupied space to the empty space of the container is

1. 5/2
2. 7/2
3. 9/2
4. 3

Correct answer: 7/2

Solution

Seven equal cylinders of radius r pack so the container radius is 3r. Occupied area = 7*pi*r^2, total = pi*(3r)^2 = 9*pi*r^2, empty = 2*pi*r^2. Ratio occupied:empty = 7/2 (option 1), not 9/2.

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