MathsCBSE Class 10 · Standard · Board exam 2025, set 30/2/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2025: question 38

Set in the CBSE Class 10 board exam of 2025, paper 30/2/1, section E, question 38, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q38 · 4 marks · Case-basedCompetency-basedSurface Areas and Volumes

Case Study – 3

A skilled carpenter decided to craft a special rolling pin for the local baker. He carefully joined three cylindrical pieces of wood – two small ones on the ends and one larger in the centre to create a perfect tool. The baker loved the rolling pin, as it rolled out the smoothest dough for breads and pastries.

The length of the bigger cylindrical part is 12 cm and diameter is 7 cm and the length of each smaller cylindrical part is 5 cm and diameter is 2·1 cm.

Based on the above information, answer the following questions :

(i)
Find the volume of the bigger cylindrical part.
1 mark
(ii)
Find the curved surface area of the bigger cylindrical part.
1 mark
(iii)(a)
Find the ratio of the volume of the bigger cylindrical part to the total volume of the two smaller (identical) cylindrical parts.
2 marks
OR
(iii)(b)
Find the sum of the curved surface areas of the two identical smaller cylindrical parts.
2 marks

Figure in the paper: Three cylinders joined end to end, shown horizontally. The central bigger cylinder has length 12 cm and diameter 7 cm. Two identical smaller cylinders at each end have length 5 cm and diameter 2.1 cm. Dimensions are labelled on each part. A photograph of a baker rolling dough with a wooden rolling pin is shown above the diagram. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/2/1.

Hints

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

Hint 1

Remember to halve each diameter to get the radius before using any formula.

Hint 2

Volume of a cylinder is $π r^{2} h$ and its curved surface area is $2 π r h$ .

Hint 3

There are two identical small cylinders, so double the result for one of them.

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.

(i) The bigger cylinder has $r = \frac{7}{2} = 3.5$ cm and $h = 12$ cm.
Volume $= π r^{2} h = \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times 12$
½ mark
(i) $= 462$ cm $^{3}$
½ mark
(ii) CSA $= 2 π r h = 2 \times \frac{22}{7} \times \frac{7}{2} \times 12$
½ mark
(ii) $= 264$ cm $^{2}$
½ mark
(iii)(a) Each smaller cylinder has $r = \frac{2.1}{2} = 1.05$ cm and $h = 5$ cm.
Total volume of the two $= 2 \times \frac{22}{7} \times 1.05 \times 1.05 \times 5$
½ mark
(iii)(a) $= 34.65$ cm $^{3}$
½ mark
(iii)(a) Ratio $= \frac{462}{34.65} = \frac{46200}{3465} = \frac{3080}{231} = \frac{40}{3}$
Required ratio $= 3080 : 231$ , i.e. 40 : 3 in simplest form.
1 mark
(iii)(b) Sum of CSAs $= 2 \times 2 π r h = 2 \times 2 \times \frac{22}{7} \times 1.05 \times 5$
1 mark
(iii)(b) $= 66$ cm $^{2}$
1 mark

Answer: (i) 462 cm³; (ii) 264 cm²; (iii)(a) 40 : 3 (= 3080 : 231), (iii)(b) 66 cm²

Where the marks are

(i) Uses $π r^{2} h$ with $r = 3.5$ and $h = 12$ (½ mark)
(i) Volume = 462 cm³ (½ mark)
(ii) Uses $2 π r h$ correctly (½ mark)
(ii) CSA = 264 cm² (½ mark)
(iii)(a) Volume of the two small cylinders set up correctly (½ mark)
(iii)(a) Total = 34.65 cm³ (½ mark)
(iii)(a) Ratio 3080 : 231, i.e. 40 : 3 (1 mark)
(iii)(b) Sets up $2 \times 2 π r h$ with $r = 1.05$ and $h = 5$ (1 mark)
(iii)(b) Total CSA = 66 cm² (1 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 paper2025 board paper, set 30/2/1 (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 2025: question 38

Hints

Step-by-step solution

Revise the chapter

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