MathsCBSE Class 10 · Basic · Board exam 2024, set 430/3/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2024: question 28(b)

Set in the CBSE Class 10 board exam of 2024, paper 430/3/1, section C, question 28(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28(b) · 3 marks · Short answerCompetency-basedSurface Areas and Volumes

A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is $2$ cm and the diameter of the base is $4$ cm. Determine the volume of the toy.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/3/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

The cone and hemisphere share the same circular base.

Hint 2

Volume of toy = volume of cone + volume of hemisphere.

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.

Radius of base (of both cone and hemisphere) $r = \frac{4}{2} = 2$ cm; height of cone $h = 2$ cm.
½ mark
Volume of cone $= \frac{1}{3} π r^{2} h = \frac{1}{3} \times \frac{22}{7} \times 4 \times 2 = \frac{176}{21}$ cm³
1 mark
Volume of hemisphere $= \frac{2}{3} π r^{3} = \frac{2}{3} \times \frac{22}{7} \times 8 = \frac{352}{21}$ cm³
1 mark
Volume of toy $= \frac{176}{21} + \frac{352}{21} = \frac{528}{21} = \frac{176}{7} \approx 25.14$ cm³
½ mark

Answer: $\frac{176}{7}$ cm³ ≈ 25.14 cm³

Where the marks are

Radius 2 cm (½ mark)
Volume of cone $\frac{1}{3} π r^{2} h$ correctly substituted (1 mark)
Volume of hemisphere $\frac{2}{3} π r^{3}$ correctly substituted (1 mark)
Total $\frac{176}{7}$ cm³ (½ mark)

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

Practise this chapterBoard-style questions from Surface Areas and Volumes, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 430/3/1 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Basic 2024: question 28(b)

Hints

Step-by-step solution

Revise the chapter

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