MathsCBSE Class 10 · Basic · Board exam 2025, set 430/1/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2025: question 34(a)

Set in the CBSE Class 10 board exam of 2025, paper 430/1/1, section D, question 34(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q34(a) · 5 marks · Long answerSurface Areas and Volumes

A toy is in the form of a cone surmounted on a hemisphere. The cone and hemisphere have the same radii. The height of the conical part of the toy is equal to the diameter of its base. If the radius of the conical part is 5 cm, find the volume of the toy.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/1/1.

Hints

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

Hint 1

The height of the cone equals the diameter, so $h = 2 r$ .

Hint 2

Add the volume of the hemisphere $\frac{2}{3} π r^{3}$ and the volume of the cone $\frac{1}{3} π r^{2} h$ .

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 $r = 5$ cm. Height of cone $h$ = diameter $= 10$ cm. Volume of toy = volume of hemisphere + volume of cone $= \frac{2}{3} π r^{3} + \frac{1}{3} π r^{2} h$ .
Volume of hemisphere $= \frac{2}{3} \times \frac{22}{7} \times 5 \times 5 \times 5 = \frac{5500}{21}$ cm³
2 marks
Volume of cone $= \frac{1}{3} \times \frac{22}{7} \times 5 \times 5 \times 10 = \frac{5500}{21}$ cm³
2 marks
Volume of toy $= \frac{5500}{21} + \frac{5500}{21} = \frac{11000}{21}$ cm³ $\approx 523.81$ cm³
1 mark

Answer: 11000/21 cm³ ≈ 523.81 cm³

Where the marks are

Correct volume of the hemisphere, $\frac{5500}{21}$ cm³ (2 marks)
Correct volume of the cone with $h = 10$ cm, $\frac{5500}{21}$ cm³ (2 marks)
Total volume $\frac{11000}{21} \approx 523.81$ cm³ (1 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 paper2025 board paper, set 430/1/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 34(a)

Hints

Step-by-step solution

Revise the chapter

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