Question 511 markSection E

  1. (ii) What is the circumference of the brooch ?

Areas Related to Circles
Circumference of a circle

Official answer

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

Answer keywords:circumferenceC = πd2πr110 cmπ = 22/7perimeter of circlebrooch

Marking scheme

  1. 1.1 mark: correct circumference = 110 cm using C=πdC = \pi d or 2πr2\pi r with π=227\pi = \frac{22}{7}.
  2. 2.Accept 110 cm; using 2πr2\pi r with r=17.5 cmr = 17.5 \text{ cm} must also give 110 cm.
  3. 3.No marks for using area formula πr2\pi r^2 instead of the perimeter formula.

Hint

Use C=πdC = \pi d with π=227\pi = \frac{22}{7}; the 35 cancels the 7 neatly.

Quick oral answer

Using C equals pi times diameter, that is 22 over 7 times 35, the seven cancels to give 22 times 5, which is 110 centimetres.

Common mistakes

  1. 1.Using the area formula πr2\pi r^2 instead of the circumference formula πd/2πr\pi d/2\pi r.
  2. 2.Using r=35r = 35 (diameter) inside 2πr2\pi r, doubling the answer to 220 cm.
  3. 3.Approximating π\pi as 3.14 and getting 109.9 cm when the intended clean answer with 227\frac{22}{7} is exactly 110 cm.

Analysis and explanation

This part tests the circumference formula applied to the outer rim of the brooch.


Concept

  • Circumference of a circle=πd=2πr\text{Circumference of a circle} = \pi d = 2\pi r; with d=35 cmd = 35 \text{ cm} and π=227\pi = \frac{22}{7}, the 7 cancels neatly to give 110 cm.

Common mistakes

  • Reaching for πr² (an area formula) instead of the perimeter formula, giving the wrong quantity (962.5) altogether.
  • Substituting the diameter in place of the radius inside 2πr, which doubles the answer to 220.

Real-world

  • The circumference is the actual length of wire a jeweller would cut to trace the boundary of the brooch; an error here also carries forward into the total-wire calculation in the next part.

Interesting facts

Because π=227\pi = \frac{22}{7} and the diameter is 35=5×735 = 5 \times 7, the circumference comes out as the exact whole number 110 cm — the numbers are engineered for a clean answer.

Circumference is the amount of wire needed just for the outer rim of the brooch, before adding the 5 internal diameters.

2πr2\pi r and πd\pi d are the same formula since d=2rd = 2r — students may use whichever they find quicker.

Question details

Q51 of 53 questions

Board
CBSE
Class
Class 10
Subject
Mathematics (Basic)
Year
2026
Section
Section E
Marks
1
Chapter
Areas Related to Circles
Topic
Circumference of a circle
Bloom's level
apply
Syllabus topic
Unit 5: Mensuration — Areas Related to Circles: Circumference (Perimeter) of a Circle
Author
CBSE
Reviewed by
Padhantu Academic Team

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Frequently asked questions

Should I use πd\pi d or 2πr2\pi r for the circumference?

Both give the same result because diameter d=2rd = 2r. With d=35 cm,πd=(227)(35)=110 cmd = 35 \text{ cm}, \pi d = \left(\frac{22}{7}\right)(35) = 110 \text{ cm}; with r=17.5 cm,2πr=2(227)(17.5)=110 cmr = 17.5 \text{ cm}, 2\pi r = 2\left(\frac{22}{7}\right)(17.5) = 110 \text{ cm}.

Why does the answer come out exactly 110 cm?

Because the diameter 35 is a multiple of 7, the 7 in π=227\pi = \frac{22}{7} cancels: (227)×35=22×5=110\left(\frac{22}{7}\right) \times 35 = 22 \times 5 = 110. CBSE picks such numbers so the answer is a neat whole number.