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In a circle of radius 21 cm, an… (Class 10 Maths 2023, Q31)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/6/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2023: question 31

Set in the CBSE Class 10 board exam of 2023, paper 30/6/1, section C, question 31, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q31 · 3 marks · Short answerAreas Related to Circles

In a circle of radius 21 cm, an arc subtends an angle of at the centre. Find the area of the sector formed by the arc. Also, find the length of the arc.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/6/1.

Hints

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

Hint 1

The sector is of the whole circle.

Hint 2

Take that fraction of for the area and of for the arc, with .

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. Area of sector cm².

    1½ marks

  2. Length of arc cm.

    1½ marks

Answer: Area of sector = 231 cm²; length of arc = 22 cm

Where the marks are

  • Uses the sector area formula and gets 231 cm² (1½ marks)
  • Uses the arc length formula and gets 22 cm (1½ marks)

Revise the chapter

Practise this chapterBoard-style questions from Areas Related to Circles, one at a time, marked against the answer key and marking points.Back to the full paper2023 board paper, set 30/6/1 (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.