MathsCBSE Class 10 · Basic · Board exam 2025, set 430/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2025: question 30(a)

Set in the CBSE Class 10 board exam of 2025, paper 430/5/1, section C, question 30(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30(a) · 3 marks · Short answerSurface Areas and Volumes

A spherical glass vessel has a cylindrical neck 7 cm long and 8 cm in diameter. The radius of spherical part is 10 cm. Find the volume of the vessel.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/5/1.

Hints

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

Hint 1

The vessel is a sphere plus a cylinder; add the two volumes.

Hint 2

Remember the neck's radius is half of 8 cm; use $\frac{4}{3} π r^{3}$ and $π r^{2} h$ .

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.

Volume of spherical part $= \frac{4}{3} π r^{3} = \frac{4}{3} \times \frac{22}{7} \times 10 \times 10 \times 10 = \frac{88000}{21} \approx 4190.48$ cm³
1 mark
Neck: radius $= \frac{8}{2} = 4$ cm, height 7 cm. Volume $= π r^{2} h = \frac{22}{7} \times 4 \times 4 \times 7 = 352$ cm³
1 mark
Volume of vessel $= 4190.48 + 352 = 4542.48$ cm³ (approx.)
1 mark

Answer: ≈ 4542.48 cm³

Where the marks are

Volume of sphere $\frac{4}{3} π (10)^{3} \approx 4190.48$ cm³ (1 mark)
Volume of cylindrical neck = 352 cm³ (1 mark)
Total volume ≈ 4542.48 cm³ (1 mark)

Revise the chapter

Chapter: Surface Areas and Volumes (notes, formulas, where marks are lost and every past question)
Topic: Cube, Cuboid and Cylinder Combination Problems

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 430/5/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 30(a)

Hints

Step-by-step solution

Revise the chapter

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