MathsCBSE Class 10 · Basic · Board exam 2024, set 430/5/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2024: question 32(b)

Set in the CBSE Class 10 board exam of 2024, paper 430/5/1, section D, question 32(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32(b) · 5 marks · Long answerSurface Areas and Volumes

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 15 cm and its base is of radius 4·2 cm, then find the total surface area of the article.

Figure in the paper: A solid cylinder standing upright. A hemispherical cavity is scooped out from the top base and another from the bottom base, shown shaded, so the article has hollow hemispherical 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 430/5/1.

Hints

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

Hint 1

When the hemispheres are scooped out, the flat circular ends are removed and replaced by hemispherical surfaces.

Hint 2

Add the curved surface of the cylinder to the curved surfaces of two hemispheres ( $2 π r^{2}$ each).

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.

Height of cylinder $h = 15$ cm; radius of cylinder = radius of each hemisphere $= r = 4.2$ cm.
1 mark
TSA of article = CSA of cylinder + CSA of 2 hemispheres $= 2 π r h + 2 (2 π r^{2}) = 2 π r h + 4 π r^{2}$
1 mark
$= 2 π r (h + 2 r) = 2 \times \frac{22}{7} \times 4.2 \times (15 + 2 \times 4.2)$
2 marks
$= 2 \times \frac{22}{7} \times 4.2 \times 23.4 = 26.4 \times 23.4 = 617.76$ cm²
1 mark

Answer: 617.76 cm²

Where the marks are

Identifies h = 15 cm and r = 4.2 cm (1 mark)
TSA = CSA of cylinder + CSA of two hemispheres (1 mark)
Correct substitution (2 marks)
Answer 617.76 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 paper2024 board paper, set 430/5/1 (Basic): 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 Basic 2024: question 32(b)

Hints

Step-by-step solution

Revise the chapter

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