The numerical value of the area of a circle is greater than the numerical value of its circumference. Is this statement true? Why

Solution:

Consider the radius of the circle as r (0 < r < 2)

Area of circle A = πr²

Where r is the radius

If r = 1.5

A = π × 1.5²

A = 2.25π

We know that

Circumference of the circle C = 2πr

Substituting the values

C = 2 × π × 1.5

C = 3π

Here C > A

Area of a circle is not always greater than the circumference.

Therefore, the statement is false.

✦ Try This: If the circumference and the area of a circle are numerically equal, then what is the numerical value of the diameter?

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12

NCERT Exemplar Class 10 Maths Exercise 11.2 Problem 7

The numerical value of the area of a circle is greater than the numerical value of its circumference. Is this statement true? Why

Summary:

The statement “The numerical value of the area of a circle is greater than the numerical value of its circumference” is false

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