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Mathematics — CBSE Class 10 board question

Q1. [2]
The largest sphere is carved out of a solid cube of side 21 cm. Find the volume of the sphere.
Previously asked in CBSE board exam
2022 30/4/1 Q6(b)
Generated by claude-sonnet-4-6 · 2026-06-15 10:36 · grounding rag
Model Answer

For the largest sphere carved from a cube of side 21 cm, the diameter of the sphere = side of cube = 21 cm, so radius $r = \dfrac{21}{2} = 10.5$ cm.

$$\text{Volume of sphere} = \frac{4}{3}\pi r^3 = \frac{4}{3} \times \frac{22}{7} \times (10.5)^3$$

$$= \frac{4}{3} \times \frac{22}{7} \times 1157.625 = 4851 \text{ cm}^3$$

Explanation

The key step is recognising that the largest sphere that fits inside a cube has its diameter equal to the side of the cube. Then apply the standard formula $V = \frac{4}{3}\pi r^3$ with $\pi = \frac{22}{7}$. Examiners award one mark for identifying $r = 10.5$ cm and one mark for the correct calculation.

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