Solve problems involving radius and diameter

A circle’s radius is the distance from its center to its circumference, while its diameter is the distance across the circle through its center; therefore, $d=2r$ and $r=\frac{d}{2}$ . Learners solve contextual and diagram-based problems by identifying the relevant measure, selecting the appropriate relationship, and reporting lengths with consistent units, without extending to more advanced circle theorems or generalized formulas.

Detailed Explanation: Solve problems involving radius and diameter

The radius is the distance from the center of a circle to its edge. The diameter is the distance all the way across the circle through its center.

They are related by:

d=2r

So:

To find the diameter, multiply the radius by $2$ .
To find the radius, divide the diameter by $2$ .

Example

A circular table has a diameter of $120\text{ cm}$ . What is its radius?

Step 1: Identify what is given and what you need.

Given: diameter, $d=120\text{ cm}$
Need: radius, $r$

Step 2: Choose the relationship.

To find the radius from the diameter, use:

r=\frac{d}{2}

Step 3: Substitute and calculate.

r=\frac{120}{2}=60\text{ cm}

Answer: The radius of the table is $\boxed{60\text{ cm}}$ . The unit stays in centimeters.

Learn by doing: Solve problems involving radius and diameter

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Circles - Find Diameter from Radius

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