MathsCBSE Class 10 · Basic · Board exam 2025, set 430/4/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2025: question 6

Set in the CBSE Class 10 board exam of 2025, paper 430/4/1, section A, question 6, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q6 · 1 mark · MCQSurface Areas and Volumes

Two right circular cylinders of equal volumes have their heights in the ratio $1 : 2$ . The ratio of their radii is:

(A) $2 : 1$
(B) $1 : 2$
(C) $1 : 4$
(D) $1 : 2$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/4/1.

Hints

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

Hint 1

The volume of a cylinder is $π r^{2} h$ .

Hint 2

Equate the two volumes and use $h_{1} : h_{2} = 1 : 2$ .

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.

Equal volumes give $π r_{1}^{2} h_{1} = π r_{2}^{2} h_{2}$ , so $\frac{r _{1}^{2}}{r _{2}^{2}} = \frac{h _{2}}{h _{1}} = \frac{2}{1}$ .
½ mark
Taking square roots, $r_{1} : r_{2} = 2 : 1$ . Hence option (A).
½ mark

Answer: $2 : 1$ , option (A)

Where the marks are

Equates the two volumes to get $r_{1}^{2} / r_{2}^{2} = 2$ (½ mark)
Concludes $r_{1} : r_{2} = 2 : 1$ (½ 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 paper2025 board paper, set 430/4/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 6

Hints

Step-by-step solution

Revise the chapter

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