Question

The area of a circle whose area and circumference are numerically equal, is 

Options

• 2 \[\pi\] sq. units 

   

• 4 \[\pi\] units 

• 6\[\pi\]sq. units 

• 8 \[\pi\] sq. units 

Answer 1

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`