MathsCBSE Class 10 · Standard · Board exam 2026, set 30/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2026: question 29(a)

Set in the CBSE Class 10 board exam of 2026, paper 30/4/1, section C, question 29(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29(a) · 3 marks · Short answerCompetency-basedSurface Areas and Volumes

To protect plants from heat, a shed of iron rods covered with green cloth is made. The lower part of the shed is a cuboid mounted by semi-cylinder as shown in the figure. Find the area of the cloth required to make this shed, if dimensions of the cuboid are 14 m × 25 m × 16 m.

Figure in the paper: A shed: cuboid with a semi-cylindrical roof on top. Front face width 14 m (semicircle of diameter 14 m on top), length 25 m, height of cuboid 16 m. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/4/1.

Hints

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

Hint 1

The cloth covers only the four side walls of the cuboid and the whole semi-cylindrical roof, including its two semicircular ends.

Hint 2

Walls: $2 (l + b) h$ . Roof: half of $2 π r h$ plus two semicircles, with $r = 7$ m.

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.

Cloth for the four walls of the cuboid (no floor, no top) $= 2 (l + b) h = 2 (14 \times 16 + 25 \times 16) = 2 (224 + 400) = 1248 m^{2}$ .
1 mark
Radius of semi-cylinder $r = \frac{14}{2} = 7$ m, length $h = 25$ m. Cloth for the semi-cylindrical part = curved surface of half-cylinder + two semicircular ends $= π r h + 2 \times \frac{1}{2} π r^{2} = \frac{22}{7} \times 7 \times 25 + \frac{22}{7} \times 7^{2}$
1 mark
$= 550 + 154 = 704 m^{2}$
½ mark
Total cloth required $= 1248 + 704 = 1952 m^{2}$ .
½ mark

Answer: 1952 m²

Where the marks are

Area of four walls = 1248 m² (1 mark)
Correct expression $π r h + π r^{2}$ for semi-cylinder with r = 7 m (1 mark)
Evaluates to 704 m² (½ mark)
Total cloth = 1952 m² (½ mark)

Revise the chapter

Chapter: Surface Areas and Volumes (notes, formulas, where marks are lost and every past question)
Topic: Surface Area and Volume Formulae Revision

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 30/4/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 29(a)

Hints

Step-by-step solution

Revise the chapter

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