Skip to content

If a cone of greatest possible… (Class 10 Maths 2025, Q14)

questionbuddy.in/q/cbse-10-maths-2025-30-6-1-q14-cone-greatest-possible-volume-hollowed

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/6/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2025: question 14

Set in the CBSE Class 10 board exam of 2025, paper 30/6/1, section A, question 14, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q14 · 1 mark · MCQSurface Areas and Volumes

If a cone of greatest possible volume is hollowed out from a solid wooden cylinder, then the ratio of the volume of remaining wood to the volume of cone hollowed out is

  1. (A)1 : 1
  2. (B)1 : 3
  3. (C)2 : 1
  4. (D)3 : 1

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/6/1.

Hints

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

Hint 1

The cone uses the same base and height as the cylinder.

Hint 2

Cone volume is one-third of the cylinder's.

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. Greatest cone has same radius r and height h as the cylinder: . Remaining .

    ½ mark

  2. Ratio . Option (C).

    ½ mark

Answer: 2 : 1, option (C)

Where the marks are

  • Remaining volume = 2/3 πr²h (½ mark)
  • Ratio 2 : 1 (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 paper2025 board paper, set 30/6/1 (Standard): 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.