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

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

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

Q29(b) · 3 marks · Short answerSurface Areas and Volumes

The internal and external radii of a hollow hemisphere are $52$ cm and 10 cm respectively. A cone of height $57$ cm and radius $52$ cm is surmounted on the hemisphere as shown in the figure. Find the total surface area of the object in terms of $π$ . (Use $2$ = 1.4)

Figure in the paper: A hollow hemisphere (shaded flat annular rim between internal and external radii) with a cone placed on its top, the cone's base lying inside the hemisphere's opening. 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

Find the slant height of the cone first using $l = r^{2} + h^{2}$ .

Hint 2

The visible surfaces are: outer hemisphere, cone's curved surface, and the flat ring between the two radii.

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.

Let internal radius $r_{1} = 52$ cm (= radius of cone) and external radius $r_{2} = 10$ cm. Slant height of the cone $l = r_{1}^{2} + h^{2} = (52)^{2} + (57)^{2} = 50 + 175 = 225 = 15$ cm.
1 mark
TSA of object = outer curved surface of hemisphere + curved surface of cone + area of the annular rim $= 2 π r_{2}^{2} + π r_{1} l + π (r_{2}^{2} - r_{1}^{2})$ $= π (2 \times 1 0^{2} + 52 \times 15 + 1 0^{2} - (52)^{2})$
1 mark
$= π (200 + 75 \times 1.4 + 100 - 50) = π (200 + 105 + 50) = 355 π cm^{2}$
1 mark

Answer: $355 π$ cm²

Where the marks are

Finds slant height $l = 15$ cm (1 mark)
Writes TSA $= 2 π r_{2}^{2} + π r_{1} l + π (r_{2}^{2} - r_{1}^{2})$ with substitution (1 mark)
Evaluates to $355 π$ cm² (1 mark)

Revise the chapter

Chapter: Surface Areas and Volumes (notes, formulas, where marks are lost and every past question)
Topic: Cone on a Hemisphere and Similar Shapes

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.

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 Standard 2026: question 29(b)

Hints

Step-by-step solution

Revise the chapter

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