MathsCBSE Class 10 · Standard · Board exam 2026, set 30/3/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2026: question 7

Set in the CBSE Class 10 board exam of 2026, paper 30/3/1, 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 cone of maximum size is carved out from a solid cube of edge length $l$ . The volume of the cone is :

(A) $\frac{π l ^{3}}{12}$
(B) $\frac{π l ^{3}}{3}$
(C) $l^{3} (1 - \frac{π}{3})$
(D) $\frac{π l ^{3}}{8}$

Figure in the paper: A cube with a cone carved out of it: the cone's circular top base lies inscribed in the top face of the cube and its vertex touches the centre of the bottom 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 30/3/1.

Hints

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

Hint 1

The base of the cone fits exactly inside one face of the cube. What is its radius?

Hint 2

Take $r = l /2$ and $h = l$ in $\frac{1}{3} π r^{2} h$ .

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.

For the largest cone, the base diameter is $l$ (so $r = \frac{l}{2}$ ) and the height is $h = l$ .
$V = \frac{1}{3} π r^{2} h = \frac{1}{3} π \cdot \frac{l ^{2}}{4} \cdot l = \frac{π l ^{3}}{12}$ , which is option (A).
1 mark

Answer: $\frac{π l ^{3}}{12}$ ; option (A)

Where the marks are

Chooses option (A) $\frac{π l ^{3}}{12}$ (1 mark)

Revise the chapter

Chapter: Surface Areas and Volumes (notes, formulas, where marks are lost and every past question)

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 30/3/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 7

Hints

Step-by-step solution

Revise the chapter

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