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A wooden article was made… (Class 10 Maths Basic 2025, Q34)

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MathsCBSE Class 10 · Basic · Board exam 2025, set 430/2/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2025: question 34

Set in the CBSE Class 10 board exam of 2025, paper 430/2/1, section D, question 34, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q34 · 5 marks · Long answerSurface Areas and Volumes

A wooden article was made by scooping out a hemisphere (of same diameter) from one end of a solid cylinder as shown in the given figure. If the height of the cylinder is 10 cm and the diameter of the cylinder is 14 cm, find the total surface area of the remaining wooden article. (Use )

Figure in the paper: A solid cylinder standing upright with height 10 cm marked along its side. A hemispherical cavity of the same diameter is scooped out of the top end, shown by a dashed hemispherical bowl inside the top of the cylinder. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/2/1.

Hints

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

Hint 1

Think about which surfaces are exposed: curved side, the uncut base, and the inside of the scooped bowl.

Hint 2

The top circular face is removed; the hemisphere's curved surface 2πr² is added.

Hint 3

Use r = 7 cm and h = 10 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. Radius of cylinder = radius of hemisphere cm; height cm.

  2. TSA of remaining article = CSA of cylinder + area of the bottom base + CSA of hemispherical cavity .

    3 marks

  3. .

    1½ marks

  4. .

    ½ mark

Answer: 902 cm²

Where the marks are

  • Correct formula with substitution (3 marks)
  • Evaluates each part: 440, 154, 308 (1½ marks)
  • Total 902 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 paper2025 board paper, set 430/2/1 (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.