What would be the radius of a circle whose area and circumference are numerically equal

Solution:

Given that the perimeter and area of the circle are numerically equal.

Let's assume a circle of radius 'r'.

Circumference of the circle = 2πr

Area of circle = πr2

The circumference of the circle and the area of the circle are equal.

Thus, we have 2πr = πr2

2 = r

Therefore, the radius of the circle is 2 units. Hence, the correct answer is A.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 12

Video Solution:

NCERT Solutions Class 10 Maths Chapter 12 Exercise 12.1 Question 5

Summary:

The radius of the circle is 2 units if the perimeter and the area of a circle are numerically equal.

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We have given that circumference and area of a circle are numerically equal.

Let it be x.

Let r be the radius of the circle, therefore, circumference of the circle is `2pi r^2`and area of the circle will bepir^2.

Therefore, from the given condition we have,

`2pir=x...............(1)`

`pir^2=x.............(2)`

Therefore, from equation (1)get r=x/2x. Now we will substitute this value in equation  

(2) we get , `pi (x/2pi)^2=x`

Simplifying further we get,

`pi xx x^2/(4pi^2)=x`

Cancelling x we get,

`pixx x^2/(4pi^2)=x`

Now we will cancel` pi`

`x/4pi=1`...........(3)

Therefore, area of the circle is `4pi sq.unit`