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Two cubes each of volume… (Class 10 Maths Basic 2024, Q32a)

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MathsCBSE Class 10 · Basic · Board exam 2024, set 430/4/1 · 5 marks · Long answer

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

Set in the CBSE Class 10 board exam of 2024, paper 430/4/1, section D, question 32(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

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

Two cubes each of volume are joined end to end. Find the volume and the surface area of the resulting cuboid.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/4/1.

Hints

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

Hint 1

Find the side of each cube from its volume. Joining the cubes does not change the total volume.

Hint 2

The cuboid's length is two sides long. Then use 2(lb + bh + hl).

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.

  1. Side of each cube: cm.

    1 mark

  2. Volume of the cuboid = volume of 2 cubes .

    1 mark

  3. Dimensions of the cuboid: cm, cm, cm.

    1½ marks

  4. Surface area

    1 mark

  5. ½ mark

Answer: Volume = 250 cm³; Surface area = 250 cm²

Where the marks are

  • Side of cube = 5 cm (1 mark)
  • Volume of cuboid = 250 cm³ (1 mark)
  • Dimensions 10 cm × 5 cm × 5 cm (1½ marks)
  • Surface area formula with substitution (1 mark)
  • Surface area = 250 cm² (½ mark)

Revise the chapter

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 430/4/1 (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.