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A solid sphere is cut into two… (Class 10 Maths 2024, Q13)

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MathsCBSE Class 10 · Standard · Board exam 2024, set 30/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2024: question 13

Set in the CBSE Class 10 board exam of 2024, paper 30/1/1, section A, question 13, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q13 · 1 mark · MCQSurface Areas and Volumes

A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres taken together, is:

  1. (A)1 : 1
  2. (B)1 : 4
  3. (C)2 : 3
  4. (D)3 : 2

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

Hints

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

Hint 1

Cutting creates two new flat circular faces.

Hint 2

TSA of a hemisphere .

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. Surface area of the sphere . Each hemisphere has total surface area , so the two together have .

  2. Ratio . The answer is option (C).

    1 mark

Answer: 2 : 3, option (C)

Where the marks are

  • Uses TSA of a hemisphere to get the ratio , option (C) (1 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 30/1/1 (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.