What is the radius of circle ?

Q: What is the radius of circle ?

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

Areas Related to Circles

Areas Related to Circles — Case Study (Silver Brooch)

Official Answer

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

radiusdiametercirclebrooch17.5 cm

Marking Scheme

11 mark: correctly stating $\text{radius} = \frac{\text{diameter}}{2} = \frac{35}{2} = 17.5 \text{ cm}$ with correct unit.

Hint

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

Quick Oral Answer

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

Analysis & Explanation

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

Concept

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

Key points

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

Common mistakes

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

Common Mistakes

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

Interesting Facts

The radius (17.5 cm) is exactly half of 35, and since $35 = 5 \times 7$ , this circle's dimensions are deliberately chosen to keep all subsequent $\pi = \frac{22}{7}$ 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.

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Frequently Asked Questions

Is the formula $r = \frac{d}{2}$ 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.