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Mathematics — CBSE Class 10 board question

Q1. [3]
A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 20 cm and the diameter of the cylinder is 7 cm. Find the total volume of the solid. (Use $\pi = \frac{22}{7}$)
Previously asked in CBSE board exam
2026 30/1/1 Q30
Generated by claude-sonnet-4-6 · 2026-06-15 10:34 · grounding rag
Model Answer

Given: Total height = 20 cm, Diameter = 7 cm → Radius (r) = 3.5 cm

The solid has a cylinder with two hemispherical ends.

Height of cylinder = Total height − 2 × radius of hemisphere
$$= 20 - 2 \times 3.5 = 13 \text{ cm}$$

Total Volume = Volume of cylinder + Volume of 2 hemispheres

$$= \pi r^2 h + 2 \times \frac{2}{3}\pi r^3 = \pi r^2 h + \frac{4}{3}\pi r^3$$

$$= \frac{22}{7} \times (3.5)^2 \times 13 + \frac{4}{3} \times \frac{22}{7} \times (3.5)^3$$

$$= \frac{22}{7} \times 12.25 \times 13 + \frac{4}{3} \times \frac{22}{7} \times 42.875$$

$$= 500.5 + 179.67 = 680.17 \text{ cm}^3 \approx 680.17 \text{ cm}^3$$

Total volume of the solid ≈ 680.17 cm³

Source: Chapter 12, Section 12.3 — Volume of a Combination of Solids

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Explanation
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