MathsCBSE Class 10 · Basic · Board exam 2026, set 430/2/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2026: question 34

Set in the CBSE Class 10 board exam of 2026, 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 $π = \frac{22}{7}$ )

Figure in the paper: A solid cylinder of height 10 cm and diameter 14 cm, with a hemispherical cavity of the same diameter scooped out from the top end (the flat face of the hemisphere is at the top circular face). See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/2/1.

Hints

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

Hint 1

The top circular face has been scooped out, so it is no longer part of the surface.

Hint 2

The remaining surfaces are the curved surface of the cylinder, the bottom base, and the inside of the hemisphere.

Hint 3

Use $2 π r h$ , $π r^{2}$ and $2 π r^{2}$ with $r = 7$ 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.

Radius $r = \frac{14}{2} = 7$ cm and height $h = 10$ cm. The TSA of the article is the curved surface of the cylinder + the bottom circular base + the inner curved surface of the hemisphere.
1 mark
CSA of cylinder $= 2 π r h = 2 \times \frac{22}{7} \times 7 \times 10 = 440$ cm².
1 mark
Area of base $= π r^{2} = \frac{22}{7} \times 7 \times 7 = 154$ cm².
1 mark
CSA of hemisphere $= 2 π r^{2} = 2 \times \frac{22}{7} \times 49 = 308$ cm².
1 mark
TSA $= 440 + 154 + 308 = 902$ cm².
1 mark

Answer: 902 cm²

Where the marks are

Identifies the three surfaces of the article (1 mark)
Finds the cylinder CSA, 440 cm² (1 mark)
Finds the base area, 154 cm² (1 mark)
Finds the hemisphere CSA, 308 cm² (1 mark)
Adds them to get 902 cm² (1 mark)

Revise the chapter

Chapter: Surface Areas and Volumes (notes, formulas, where marks are lost and every past question)
Topic: Surface Area of a Combination of Solids

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 paper2026 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.

CBSE Class 10 Mathematics Basic 2026: question 34

Hints

Step-by-step solution

Revise the chapter

More questions from Surface Areas and Volumes