MathsCBSE Class 10 · Basic · Sample paper, session 2023-24 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic sample paper 2023-24: question 34(b)

From the official CBSE sample question paper for 2023-24, section D, question 34(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q34(b) · 5 marks · Long answerCompetency-basedSurface Areas and Volumes

A gulab jamun contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.

Figure in the paper: Photograph-style figure of a glass (tumbler) filled with syrup, containing several gulab jamuns submerged in it. Each gulab jamun is cylindrical with hemispherical ends, labelled with length 5 cm and diameter 2.8 cm in the question. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

The length 5 cm includes both hemispherical ends, so the cylinder's height is 5 − 2.8 cm.

Hint 2

Find the volume of one gulab jamun, multiply by 45, then take 30% of it.

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.

Radius of cylinder = radius of hemisphere $= \frac{2.8}{2} = 1.4$ cm.
Height of cylinder $= 5 - 2 (1.4) = 5 - 2.8 = 2.2$ cm.
1 mark
Volume of one gulab jamun = volume of cylinder + 2 × volume of hemisphere $= π r^{2} h + 2 \times \frac{2}{3} π r^{3}$
1 mark
$= \frac{22}{7} \times (1.4)^{2} \times 2.2 + 2 \times \frac{2}{3} \times \frac{22}{7} \times (1.4)^{3} \approx 13.55 + 11.50 = 25.05 cm^{3}$
1 mark
Volume of syrup in 45 gulab jamuns $= \frac{30}{100} \times 45 \times 25.05 = 338.175 cm^{3} \approx 338 cm^{3}$
2 marks

Answer: Approximately 338 cm³ of syrup

Where the marks are

Radius 1.4 cm and cylinder height 2.2 cm (1 mark)
Volume formula: cylinder + two hemispheres (1 mark)
Volume of one gulab jamun ≈ 25.05 cm³ (1 mark)
30% of the volume of 45 gulab jamuns ≈ 338 cm³ (2 marks)

Revise the chapter

Chapter: Surface Areas and Volumes (notes, formulas, where marks are lost and every past question)
Topic: Volume of a Combination of Solids

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 paperSample paper 2023-24 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2023-24: question 34(b)

Hints

Step-by-step solution

Revise the chapter

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