MathsCBSE Class 10 · Standard · Board exam 2025, set 30/4/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2025: question 34

Set in the CBSE Class 10 board exam of 2025, paper 30/4/1, section D, question 34, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q34 · 5 marks · Long answerCompetency-basedSurface Areas and Volumes

A wooden cubical die is formed by forming hemispherical depressions on each face of the cube such that face 1 has one depression, face 2 has two depressions and so on. The sum of number of hemispherical depressions on opposite faces is always 7. If the edge of the cubical die measures 5 cm and each hemispherical depression is of diameter 1.4 cm, find the total surface area of the die so formed.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/4/1.

Hints

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

Hint 1

Count the depressions on all six faces: 1 to 6.

Hint 2

Each depression removes a flat circle $π r^{2}$ from the cube's surface but adds a curved surface $2 π r^{2}$ .

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.

Number of depressions $= 1 + 2 + 3 + 4 + 5 + 6 = 21$ . Radius of each $r = 0.7$ cm.
1 mark
TSA of die = TSA of cube + CSA of 21 hemispheres − area of 21 circular openings.
TSA of cube $= 6 \times 5^{2} = 150$ cm²
1 mark
CSA of 21 hemispheres $= 21 \times 2 π r^{2} = 21 \times 2 \times \frac{22}{7} \times (0.7)^{2} = 64.68$ cm²
1 mark
Area of 21 circular bases removed $= 21 \times π r^{2} = 21 \times \frac{22}{7} \times (0.7)^{2} = 32.34$ cm²
1 mark
TSA $= 150 + 64.68 - 32.34 = 182.34$ cm²
1 mark

Answer: 182.34 cm²

Where the marks are

Total depressions = 21 (1 mark)
TSA of cube = 150 cm² (1 mark)
CSA of 21 hemispheres = 64.68 cm² (1 mark)
Base area of 21 depressions = 32.34 cm² (1 mark)
Total surface area 182.34 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 30/4/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 34

Hints

Step-by-step solution

Revise the chapter

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