CBSE Class 10 Mathematics Standard sample paper 2025-26: question 34(B)

Hints

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Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

1. Volume of the cone $=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi \times 3\times 3\times 12=36\pi$ cm³

   The lower $\frac{1}{6}$ of the cone is empty, so the ice-cream fills $\frac{5}{6}$ of it:

   $\frac{5}{6}\times 36\pi =30\pi$ cm³

   2 marks

2. Hemisphere on top. Its radius equals the cone's radius, $r=3$ cm.

   Volume $=\frac{2}{3}\pi r^3=\frac{2}{3}\pi \times 27=18\pi$ cm³

   1½ marks

3. Total volume of ice-cream $=30\pi +18\pi =48\pi$ cm³

   $=48\times \frac{22}{7}\approx 150.86$ cm³

   1½ marks

Answer: $48\pi$ cm³ ≈ 150.86 cm³

Revise the chapter

• Chapter: Surface Areas and Volumes (notes, formulas, where marks are lost and every past question)
• Topic: Cone on a Hemisphere and Similar Shapes