Three tennis balls are just packed in a cylindrical jar. If radius of each ball is $r$, volume of air inside the jar is
Generated by claude-sonnet-4-6 · 2026-06-15 10:32 · grounding rag
Model Answer
Option (D) $4\pi r^3$
Volume of cylinder (radius $r$, height $6r$) $= \pi r^2 \times 6r = 6\pi r^3$.
Volume of 3 spheres $= 3 \times \dfrac{4}{3}\pi r^3 = 4\pi r^3$.
Volume of air $= 6\pi r^3 - 4\pi r^3 = \mathbf{4\pi r^3}$.
Source: Chapter 12, Section 12.3
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Explanation
- Three balls stacked in a cylinder means the cylinder's height = $3 \times 2r = 6r$ and radius = $r$.
- Subtract total sphere volume from cylinder volume to get air space.
- Examiners expect the setup (cylinder dimensions), the subtraction, and the correct answer. Do not confuse diameter with radius when setting up cylinder height.