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Volume of Empty Space in Cylinder

CMAT 2025 · Quantitative Techniques & Data Interpretation · Medium · Quantitative Techniques

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A cylindrical box of radius 5 cm contains 10 solid spherical balls, each of radius 5 cm. If the top most ball touches the upper cover of the box, then the volume of empty space in the box is:

  1. A.

    2500/3 \pi cm^3

  2. B.

    5000 \pi cm^3

  3. C.

    2500 \pi cm^3

  4. D.

    5000/3 \pi cm^3

Answer

A

Explanation

Height of the cylinder = 10×2r=10×10=10010 \times 2r = 10 \times 10 = 100 cm. Volume of cylinder = πr2h=π(52)(100)=2500π\pi r^2 h = \pi (5^2) (100) = 2500\pi cm3^3. Volume of 10 spherical balls = 10×43π(53)=50003π10 \times \frac{4}{3}\pi (5^3) = \frac{5000}{3}\pi cm3^3. Volume of empty space = 2500π−50003π=25003π2500\pi - \frac{5000}{3}\pi = \frac{2500}{3}\pi cm3^3.

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