medium difficulty5 min

Choosing formula based on context

Choosing formula based on context means identifying whether the question asks for area, length, perimeter, or a part of a circle before calculating.

In one line: Around means length, inside means area.

Practice This Concept

Understand it

The same circle can lead to different formulas depending on what is asked.
If the question asks for boundary length, use circumference or arc length.
If it asks for space covered, use area.
Good students first identify the quantity, then select the formula.

Example

For a circular track, the distance around is circumference, but the ground covered inside is area.

Formula and rule

Boundary words suggest circumference or arc length.

Inside-space words suggest area of circle, sector, semicircle, quadrant, or segment.

See it worked out

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

Worked example

1If the question says 'how much paper covers the sticker?', use area.
2If it says 'how much ribbon goes around it?', use circumference.

Method you can reuse

1Read the asking word carefully.
2Decide whether the quantity is area or length.
3Identify the exact circle part.
4Pick the matching formula.
5Then calculate.

Sketch it in your answer

Mark the asked part in the figure: boundary, arc, sector, shaded part, or complete inside region.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

A question asks for the space inside a circular sticker. Which formula should you think of first?

Think first, then show answer

You should think of the area of a circle first, because 'space inside' refers to the surface enclosed by the circle, not its boundary.

Common wrong answer

A common wrong answer is to use area formula for a boundary question or circumference formula for a covering question.

Don't mix this up

Students often know the formulas but choose the wrong one because they rush to calculate without reading the question carefully.

Exam tip

Underline words like around, inside, arc, sector, shaded, boundary, and covering. These words point to the right formula.

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

Choose the correct formula from a word problem, especially when both area and length formulas are nearby.

1
Enough for 1 mark
Choosing formula based on context means identifying whether the question asks for area, length, perimeter, or a part of a circle before calculating.
2
Add for 2 marks
Example: For a circular track, the distance around is circumference, but the ground covered inside is area.
3
Add for 3 marks
The same circle can lead to different formulas depending on what is asked.

MCQ Quiz

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