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From each end of a solid… (Class 10 Maths Basic 2025, Q30b)

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

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

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

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

From each end of a solid cylinder of height 20 cm and base radius 7 cm, a cone of base radius 2.1 cm and height 5 cm is scooped out. Find the volume of the remaining solid.

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

Remaining volume = volume of cylinder − volume of the cones removed.

Hint 2

There are two cones (one from each end); use with cm, cm.

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 cylinder cm³

    1 mark

  2. Volume of two cones cm³

    1 mark

  3. Volume of remaining solid cm³

    1 mark

Answer: 3033.8 cm³

Where the marks are

  • Volume of cylinder = 3080 cm³ (1 mark)
  • Volume of the two cones = 46.2 cm³ (1 mark)
  • Remaining volume = 3033.8 cm³ (1 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 paper2025 board paper, set 430/5/1 (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.