Find the length of the arc of a circle which subtends an angle of 60° at the centre of the circle of radius 42 cm.

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2024: question 22(b)

Set in the CBSE Class 10 board exam of 2024, paper 30/4/1, section B, question 22(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(b) · 2 marks · Very short answerAreas Related to Circles

Find the length of the arc of a circle which subtends an angle of $6 0^{\circ}$ at the centre of the circle of radius 42 cm.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/4/1.

Hints

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

Hint 1

An arc is a fraction of the whole circumference.

Hint 2

Use $l = \frac{θ}{360} \times 2 π r$ with $θ = 6 0^{\circ}$ , $r = 42$ 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.

Length of arc $= \frac{θ}{36 0 ^{\circ}} \times 2 π r = \frac{60}{360} \times 2 \times \frac{22}{7} \times 42$
1½ marks
$= \frac{1}{6} \times 264 = 44$ cm
½ mark

Answer: 44 cm

Where the marks are

Correct arc-length formula with substitution (1½ marks)
Arc length = 44 cm (½ mark)

Revise the chapter

Chapter: Areas Related to Circles (notes, formulas, where marks are lost and every past question)
Topic: Length of an Arc of a Circle

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 paper2024 board paper, set 30/4/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 22(b)

Hints

Step-by-step solution

Revise the chapter

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