CBSE Class 10 Mathematics Standard 2026: question 30

Hints

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Step-by-step solution

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1. Radius of cylinder = radius of each hemisphere $=r=\frac{7}{2}$ cm.

   ½ mark

2. Total height = 20 cm. Each hemispherical end adds height $r$.

   Height of cylinder $h=20-\frac{7}{2}-\frac{7}{2}=13$ cm.

   ½ mark

3. Volume of solid = volume of cylinder + volume of 2 hemispheres:
   $$V=\pi r^{2}h+2\times \frac{2}{3}\pi r^3=\frac{22}{7}\times {\left(\frac{7}{2}\right)}^2\times 13+2\times \frac{2}{3}\times \frac{22}{7}\times {\left(\frac{7}{2}\right)}^3$$

   1 mark

4. Take $\pi r^2$ common:
   $$V=\frac{22}{7}\times \frac{49}{4}\times \left(13+\frac{4}{3}\times \frac{7}{2}\right)=\frac{77}{2}\times \left(13+\frac{14}{3}\right)=\frac{77}{2}\times \frac{53}{3}$$
   $$V=\frac{4081}{6}\approx 680.17{\text{ cm}}^3$$

   1 mark

Answer: Volume = $\frac{4081}{6}$ cm³ ≈ 680.17 cm³

Revise the chapter

• Chapter: Surface Areas and Volumes (notes, formulas, where marks are lost and every past question)
• Topic: Volume of a Combination of Solids