GATE CE 2024 Set 2 — Question 7
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General Aptitude → Quantitative Aptitude → Mensuration & Geometry
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Question
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
Correct answer
(B) 7/2
Solution
Let the radius of each chalk-stick be .
1.The arrangement shows a central chalk-stick surrounded by six others. The distance from the center of the central stick to the center of any outer stick is .
2.The radius of the outer cylindrical container must be to fit them tightly.
3.Let the length of the sticks and container be .
4.Volume of the 7 chalk-sticks (occupied space) = .
5.Total volume of the container = .
6.Empty space = Total volume Occupied space = .
7.Ratio of occupied space to empty space = .
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