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.

Areas Related to Circles

Radius from diameter

Official Answer

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

radiusdiameter35 cm17.5 cmr = d/2circlebrooch

Marking Scheme

11 mark: correct $\text{radius} = 17.5 \text{ cm}$ (with unit). Accept $\frac{35}{2} \text{ cm}$ or 17.5 cm.
2No 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.

Analysis & Explanation

This opening part of the brooch case study checks the most basic circle relationship and sets up every later calculation.

Concept

Diameter = 2 × radius, so radius = diameter ÷ 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.

Common Mistakes

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

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.

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Frequently Asked Questions

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 $d = 35 \text{ cm}, r = \frac{35}{2} = 17.5 \text{ cm}$ .

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.