MathsCBSE Class 10 · Standard · Board exam 2026, set 30/5/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2026: question 7

Set in the CBSE Class 10 board exam of 2026, paper 30/5/1, section A, question 7, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q7 · 1 mark · MCQSurface Areas and Volumes

A conical cavity of maximum volume is carved out from a wooden solid hemisphere of radius 10 cm. Curved surface area of the cavity carved out is (use $π = 3.14$ )

(A) $3142$ cm $^{2}$
(B) $314$ cm $^{2}$
(C) $\frac{3140}{3}$ cm $^{2}$
(D) $31402$ cm $^{2}$

Figure in the paper: A solid hemisphere shown with its flat circular face at the top. A cone is inscribed inside it: its apex touches the curved surface at the bottom, and its circular base lies on the flat top face. A vertical axis line joins the centre of the top face to the bottom apex. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/5/1.

Hints

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

Hint 1

The cone's radius and height both equal the hemisphere's radius.

Hint 2

Find slant height, then use $π r l$ .

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.

Maximum cone: $r = 10$ cm, $h = 10$ cm, so $l = 1 0^{2} + 1 0^{2} = 102$ cm.
CSA $= π r l = 3.14 \times 10 \times 102 = 3142$ cm $^{2}$ , option (A).
1 mark

Answer: $3142$ cm $^{2}$ , option (A)

Where the marks are

Takes $r = h = 10$ , $l = 102$ and computes $π r l$ (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 30/5/1 (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 7

Hints

Step-by-step solution

Revise the chapter

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