Question 541 markSection E

What is the circumference of the brooch ?

Areas Related to Circles
Areas Related to Circles — Case Study (Silver Brooch)

Official answer

Circumference = 110 cm, using C=πd=(227)×35=110 cmC = \pi d = \left(\frac{22}{7}\right) \times 35 = 110 \text{ cm}.

Answer keywords:circumferencecirclebroochpi22/7diameter110 cm

Marking scheme

  1. 1.1 mark: correct formula C = πd (or 2πr) with π = 22/7 correctly substituted, and correct final value 110 cm with unit.

Hint

Use C=πdC = \pi d with π=227\pi = \frac{22}{7} (since 35 is a multiple of 7) for an exact answer — do not use 3.14.

Quick oral answer

Circumference equals π times the diameter; since 35 is a multiple of 7, using π=227\pi = \frac{22}{7} gives 227×35=110 cm\frac{22}{7} \times 35 = 110 \text{ cm} exactly.

Common mistakes

  1. 1.Using π=3.14\pi = 3.14 instead of 227\frac{22}{7}, giving an inexact decimal answer (≈109.9 cm)(\approx 109.9 \text{ cm}) instead of the clean intended value of 110 cm.
  2. 2.Using the radius (17.5 cm) in the formula C=πdC = \pi d instead of C=2πrC = 2\pi r, i.e., forgetting to double the radius or mistakenly using d twice.
  3. 3.Arithmetic slip while cancelling 357=5\frac{35}{7} = 5.

Analysis and explanation

Find the circumference of the brooch using C=πdC = \pi d.


Concept

  • Circumference formula: C=πdC = \pi d (equivalently 2πr2\pi r).
  • Diameter = 35 cm is a multiple of 7, so π=227\pi = \frac{22}{7} gives an exact answer.

Key points

  • C=(227)×35=22×5=110 cmC = \left(\frac{22}{7}\right) \times 35 = 22 \times 5 = 110 \text{ cm} — no rounding needed.
  • This length represents only the outer rim wire, not the 5 internal diameter wires.

Common mistakes

  • Using π=3.14\pi = 3.14 instead of 22/7, giving an inexact 109.9 cm rather than the intended exact 110 cm.

Interesting facts

The circumference (110 cm) represents the exact length of silver wire that would be needed just for the outer rim of the brooch, excluding the wire used for the internal diameters.

The constant π was first approximated as 22/7 by the Greek mathematician Archimedes around 250 BCE, and it remains the standard fraction used in Indian school mathematics for exact-answer problems.

Question details

Q54 of 56 questions

Board
CBSE
Class
Class 10
Subject
Mathematics (Standard)
Year
2026
Section
Section E
Marks
1
Chapter
Areas Related to Circles
Topic
Areas Related to Circles — Case Study (Silver Brooch)
Bloom's level
apply
Syllabus topic
Unit 6: Mensuration — Areas Related to Circles: circumference of a circle
Author
CBSE
Reviewed by
Padhantu Academic Team

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Frequently asked questions

Why use 227\frac{22}{7} instead of 3.14 for pi here?

Because the diameter (35 cm) is a multiple of 7, using π=227\pi = \frac{22}{7} cancels exactly to give a clean whole-number answer (110 cm), which is the standard CBSE convention for such values.

Does the circumference include the 5 internal diameters of wire?

No — circumference refers only to the length of the outer circular boundary of the brooch, not the 5 internal diameter wires that create the 10 sectors.