NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 11: Area Related To Circles - Exercise 11.2

Question 7

Step 1: Recall the formulas

For a circle of radius \(r\) metres:

• Area = \(\pi r^2\) square metres (\(m^2\))
• Circumference = \(2\pi r\) metres (\(m\))

Step 2: Compare their numerical values

We are not comparing the units (since area and length are different quantities), but only the numbers that come in front of the units.

So, compare: \(\pi r^2\) (number from area) and \(2\pi r\) (number from circumference).

Step 3: Cancel common factor

Both expressions have \(\pi\). Divide both sides by \(\pi\):

Compare \(r^2\) with \(2r\).

Step 4: Simplify

Divide both sides by \(r\) (assuming \(r > 0\)):

Compare \(r\) with 2.

Step 5: Interpret

• If \(r > 2\) m → Area number > Circumference number
• If \(r = 2\) m → Area number = Circumference number
• If \(r < 2\) m → Area number < Circumference number

Step 6: Conclusion

The statement says “the area is greater than the circumference” as if it is always true. But it depends on the radius:

Only for radii greater than 2 m is the area number larger. For smaller radii, it is not.

Therefore, the statement is False.