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GATE 2024 IN – Question 7

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Seven identical cylindrical chalk-sticks are fitted tightly in a cylindrical container, as shown. The container has the same length as the chalk-sticks. The ratio of occupied space to empty space is

Diagram for GATE 2024 IN question 7
  1. $5/2$
  2. $7/2$
  3. $9/2$
  4. 3

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Show answer and explanation

Correct answer: (B) $7/2$

Explanation

Let a chalk-stick have radius $r$ and length $L$. The six outer centres are $2r$ from the central centre, so the container radius is $3r$. Container volume is $9\pi r^2L$ and chalk volume is $7\pi r^2L$. Empty volume is $2\pi r^2L$, giving occupied/empty $=7/2$, **B**.