Question 501 markSection E

$Case Study - 3. A brooch is crafted from silver wire in the shape of a circle with a diameter of 35 cm. The wire is also used to create 5 diameters, dividing the circle into 10 equal sectors as shown in figure. (i) What is the radius of circle ?$

Q: 38. Case Study - 3. A brooch is crafted from silver wire in the shape of a circle with a diameter of 35 cm. The wire is also used to create 5 diameters, dividing the circle into 10 equal sectors as shown in figure. (i) What is the radius of circle ?

$\text{Radius} = 17.5 \text{ cm}$, obtained by halving the given diameter of 35 cm.

Q: How do you get the radius from the diameter?

The diameter passes through the centre and equals twice the radius, so $\text{radius} = \text{diameter} \div 2$. For $d = 35 \text{ cm}, r = \frac{35}{2} = 17.5 \text{ cm}$.

Q: Why is the answer a decimal (17.5 cm)?

Because 35 is an odd number, half of it is 17.5. This is perfectly acceptable; you keep 17.5 cm and it will simplify nicely with $\pi = \frac{22}{7}$ in the circumference and area parts.

Areas Related to Circles

Radius from diameter

Official answer

\text{Radius} = 17.5 \text{ cm}

radius

diameter

35 cm

17.5 cm

r = d/2

circle

brooch

Marking scheme

1. $\text{radius} = 17.5 \text{ cm}$
2. $No marks if diameter (35 cm) is written as the radius.$

Hint

$Radius is always half of the diameter — just divide 35 by 2.$

Quick oral answer

$The radius is half the diameter, so 35 divided by 2 gives 17.5 centimetres.$

Common mistakes

1. $Writing 35 cm (the diameter) as the radius instead of halving it.$
2. $Doubling instead of halving — giving 70 cm.$
3. $Dropping the unit cm.$

Analysis and explanation

This opening part of the brooch case study checks the most basic circle relationship and sets up every later calculation. Concept Diameter = 2 \times radius, so radius = diameter \div 2. Here diameter = 35 cm, a multiple of 7, chosen so π = 22/7 later gives clean arithmetic. Common mistakes Copying the diameter (35 cm) directly as the radius under exam pressure, which then doubles the circumference and quadruples the area in later parts. Real-world Jewellers and engineers specify circular parts by diameter (easy to measure with callipers) but must convert to radius for any area or arc-length calculation, exactly as tested here.

Interesting facts

$The word 'radius' is Latin for the spoke of a wheel — here the 5 diameters really do look like wheel spokes crossing the centre.$

$With diameter 35 cm the number is chosen so that 35 is a multiple of 7, which makes π = 22/7 cancel neatly in later parts.$

$A real silver brooch of 35 cm diameter would be unusually large — CBSE scales up the numbers to keep the arithmetic clean.$

Question details

Q50 of 53 questions

Board: CBSE
Class: Class 10
Subject: Mathematics (Basic)
Year: 2026
Section: Section E
Marks: 1
Chapter: Areas Related to Circles
Topic: $Radius from diameter$
Bloom's level: understand
Syllabus topic: $Unit 5: Mensuration — Areas Related to Circles: Radius and Diameter of a Circle$
Author: CBSE
Reviewed by: Padhantu Academic Team

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Frequently asked questions

$How do you get the radius from the diameter?$

$\text{radius} = \text{diameter} \div 2$

$Why is the answer a decimal (17.5 cm)?$

$\pi = \frac{22}{7}$