MathsCBSE Class 10 · Standard · Board exam 2025, set 30/5/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2025: question 34(a)

Set in the CBSE Class 10 board exam of 2025, paper 30/5/1, section D, question 34(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q34(a) · 5 marks · Long answerSurface Areas and Volumes

From one of the faces of a solid wooden cube of side 14 cm, maximum number of hemispheres of diameter 1.4 cm are scooped out. Find the total number of hemispheres that can be scooped out. Also, find the total surface area of the remaining solid.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/5/1.

Hints

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

Hint 1

How many diameters of 1.4 cm fit along a 14 cm edge? Do the same for the other edge.

Hint 2

Scooping removes the flat circular area but adds the curved surface of each hemisphere.

Hint 3

Use $2 π r^{2}$ for the curved surface of a hemisphere and $π r^{2}$ for a circle, with r = 0.7 cm.

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.

Each hemisphere of diameter 1.4 cm occupies a $1.4 \times 1.4$ square on the face. Number of hemispheres $= \frac{14 \times 14}{1.4 \times 1.4}$
1 mark
$= 10 \times 10 = 100$
1 mark
TSA of remaining solid = TSA of cube + CSA of 100 hemispheres − area of 100 circular tops, with $r = 0.7$ cm: $= 6 \times 14 \times 14 + 100 \times 2 \times \frac{22}{7} \times 0.7 \times 0.7 - 100 \times \frac{22}{7} \times 0.7 \times 0.7 = 1176 + 308 - 154$
2 marks
$= 1330 cm^{2}$
1 mark

Answer: 100 hemispheres; TSA = 1330 cm²

Where the marks are

Sets up the count $\frac{14 \times 14}{1.4 \times 1.4}$ (1 mark)
Gets 100 hemispheres (1 mark)
Correct TSA expression: cube + hemisphere CSA − circles (2 marks)
TSA = 1330 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 30/5/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 34(a)

Hints

Step-by-step solution

Revise the chapter

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