MathsCBSE Class 10 · Standard · Board exam 2024, set 30/5/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2024: question 35

Set in the CBSE Class 10 board exam of 2024, paper 30/5/1, section D, question 35, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q35 · 5 marks · Long answerSurface Areas and Volumes

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the figure. If the height of the cylinder is $5 \cdot 8$ cm and its base is of radius $2 \cdot 1$ cm, find the total surface area of the article.

Figure in the paper: A solid cylinder standing upright with a hemispherical cavity scooped out of the top end and another hemispherical cavity scooped out of the bottom end. The cavities are shown as shaded hemispherical bowls at both ends. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/5/1.

Hints

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

Hint 1

Think about which surfaces are visible: the curved side of the cylinder and the inside of the two bowls. The flat circular ends are removed.

Hint 2

Each hemispherical cavity has curved surface area $2 π r^{2}$ ; add both to $2 π r h$ .

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.

TSA of article = CSA of cylinder + CSA of two hemispherical cavities (r = 2.1 cm, h = 5.8 cm).
CSA of cylinder $= 2 π r h = 2 \times \frac{22}{7} \times 2.1 \times 5.8$
1 mark
$= 13.2 \times 5.8 = 76.56$ cm²
1 mark
CSA of two hemispheres $= 2 \times 2 π r^{2} = 4 \times \frac{22}{7} \times 2.1 \times 2.1$
1 mark
$= 4 \times 13.86 = 55.44$ cm²
1 mark
Total surface area of article $= 76.56 + 55.44 = 132$ cm²
1 mark

Answer: 132 cm²

Where the marks are

Writes CSA of cylinder $2 π r h$ with values (1 mark)
CSA of cylinder = 76.56 cm² (1 mark)
Writes CSA of two hemispheres $4 π r^{2}$ with values (1 mark)
= 55.44 cm² (1 mark)
TSA = 132 cm² (1 mark)

Revise the chapter

Chapter: Surface Areas and Volumes (notes, formulas, where marks are lost and every past question)
Topic: Surface Area 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 paper2024 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 2024: question 35

Hints

Step-by-step solution

Revise the chapter

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