MathsCBSE Class 10 · Basic · Board exam 2024, set 430/2/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2024: question 31

Set in the CBSE Class 10 board exam of 2024, paper 430/2/1, 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

A car has two wipers which do not overlap. Each wiper has a blade of length 21 cm sweeping through an angle of $12 0^{\circ}$ . Find the area cleaned at each sweep of the blades.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/2/1.

Hints

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

Hint 1

The region swept by one blade is a sector of a circle.

Hint 2

Area of a sector $= \frac{θ}{36 0 ^{\circ}} π r^{2}$ , with $r$ equal to the blade length.

Hint 3

There are two wipers that do not overlap, so combine their areas.

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.

Each wiper sweeps a sector with $r = 21$ cm and $θ = 12 0^{\circ}$ .
½ mark
Area swept by one wiper $= \frac{θ}{36 0 ^{\circ}} \times π r^{2} = \frac{120}{360} \times \frac{22}{7} \times 21 \times 21$
1½ marks
$= \frac{1}{3} \times 22 \times 3 \times 21 = 462$ cm²
½ mark
The wipers do not overlap, so the total area cleaned at each sweep $= 2 \times 462 = 924$ cm².
½ mark

Answer: 924 cm² (462 cm² by each wiper)

Where the marks are

Identifies $r = 21$ cm and $θ = 12 0^{\circ}$ (½ mark)
Uses the sector area formula with correct substitution (1½ marks)
Area for one wiper = 462 cm² (½ mark)
Total area for both wipers = 924 cm² (½ mark)

Revise the chapter

Chapter: Areas Related to Circles (notes, formulas, where marks are lost and every past question)
Topic: Area of a Sector 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 430/2/1 (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.

CBSE Class 10 Mathematics Basic 2024: question 31

Hints

Step-by-step solution

Revise the chapter

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