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A vessel is in the form… (Class 10 Maths Basic 2024, Q28a)

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

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

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

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

A vessel is in the form of a hollow hemisphere surmounted by a hollow cylinder. The diameter of the hemisphere is cm and the total height of the vessel is cm. Find the inner surface area of the vessel.

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 total height includes the hemisphere's height, which equals its radius.

Hint 2

Inner surface = curved surface of cylinder + curved surface of hemisphere (no top, no base).

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. Radius cm. Height of cylindrical part cm.

    ½ mark

  2. Inner curved surface area of cylinder cm²

    1 mark

  3. Inner curved surface area of hemisphere cm²

    1 mark

  4. Inner surface area of vessel cm²

    ½ mark

Answer: 572 cm²

Where the marks are

  • Finds cm and cylinder height 6 cm (½ mark)
  • CSA of cylinder cm² (1 mark)
  • CSA of hemisphere cm² (1 mark)
  • Total 572 cm² (½ mark)

Revise the chapter

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.