Question 531 markSection E

What is the radius of circle ?

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

Official answer

Radius=17.5 cm\text{Radius} = 17.5 \text{ cm}, since radius=diameter2=352\text{radius} = \frac{\text{diameter}}{2} = \frac{35}{2}.

Answer keywords:radiusdiametercirclebrooch17.5 cm

Marking scheme

  1. 1.1 mark: correctly stating radius=diameter2=352=17.5 cm\text{radius} = \frac{\text{diameter}}{2} = \frac{35}{2} = 17.5 \text{ cm} with correct unit.

Hint

Radius is always exactly half the diameter: r=d2r = \frac{d}{2}.

Quick oral answer

The radius is simply half the diameter, so 35 cm÷2=17.5 cm35 \text{ cm} \div 2 = 17.5 \text{ cm}.

Common mistakes

  1. 1.Forgetting to divide the diameter by 2 and writing 35 cm as the radius.
  2. 2.Decimal-point errors such as writing 1.75 cm or 175 cm instead of 17.5 cm.
  3. 3.Omitting the unit (cm) in the final answer.

Analysis and explanation

Find the radius of the brooch's circle from its given diameter.


Concept

  • Radius=diameter÷2\text{Radius} = \text{diameter} \div 2, the most basic circle relationship.

Key points

  • Diameter=35 cm⇒radius=352=17.5 cm\text{Diameter} = 35 \text{ cm} \Rightarrow \text{radius} = \frac{35}{2} = 17.5 \text{ cm}; this value feeds every later calculation in the case study.

Common mistakes

  • Writing radius=diameter\text{radius} = \text{diameter} (forgetting to halve).
  • Decimal slip: writing 1.75 cm or 175 cm instead of 17.5 cm.

Interesting facts

The radius (17.5 cm) is exactly half of 35, and since 35=5×735 = 5 \times 7, this circle's dimensions are deliberately chosen to keep all subsequent π=227\pi = \frac{22}{7} calculations in the case study free of ugly decimals.

In jewellery design, the radius of a circular brooch directly determines how much metal wire is needed for the outer rim.

Question details

Q53 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
remember
Syllabus topic
Unit 6: Mensuration — Areas Related to Circles: relationship between diameter and radius
Author
CBSE
Reviewed by
Padhantu Academic Team

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Frequently asked questions

Is the formula r=d2r = \frac{d}{2} always true for any circle?

Yes, the radius is always exactly half the diameter for every circle, regardless of size.

Why does the radius come out as a clean decimal (17.5) rather than a whole number?

Because the given diameter, 35 cm, is an odd number; dividing an odd number by 2 always gives a value ending in .5.