medium difficulty5 min

Converting units in circle measures

Converting units in circle measures means changing radius, diameter, area, or length into compatible units before calculation.

In one line: Same units first, smart formula next.

Practice This Concept

Understand it

Circle problems become wrong very quickly when units are mixed. A radius in cm and a length asked in m cannot be used directly without conversion. Students should first convert all quantities into the same unit system, then apply the formula.

Example

If radius is 70 mm, convert it to 7 cm before using πr² in cm² if the answer is expected in cm².

Formula and rule

Use 10 mm = 1 cm, 100 cm = 1 m, and keep all length units consistent before applying circle formulas.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

1Radius = 35 mm = 3.5 cm.
2Area = π × 3.5² = 12.25π cm² = 38.5 cm².

Method you can reuse

1Read all units carefully.
2Convert every length to one common unit.
3Apply the correct formula.
4Use square units for area answers.
5Recheck the final unit.

Sketch it in your answer

Write unit labels beside radius, diameter, arc length, or area values in the diagram so conversion is not missed.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

A radius is given as 250 mm, but the answer is needed in cm. What should you do first?

Think first, then show answer

You should convert 250 mm into 25 cm first, because the formula must use one unit system consistently before you calculate area or circumference.

Common wrong answer

A common wrong answer is to treat 250 mm as 250 cm and produce a much larger value than expected.

Don't mix this up

Students often multiply numbers correctly but forget to convert mm to cm or cm to m first.

Exam tip

Check units before calculation, not after calculation. This saves marks in final answer lines.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Convert units and then find area, circumference, arc length, or perimeter of a sector or circle part.

1
Enough for 1 mark
Converting units in circle measures means changing radius, diameter, area, or length into compatible units before calculation.
2
Add for 2 marks
Example: If radius is 70 mm, convert it to 7 cm before using πr² in cm² if the answer is expected in cm².
3
Add for 3 marks
Circle problems become wrong very quickly when units are mixed.

MCQ Quiz

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