Question

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

(a) 2$\mathrm{\pi }$ sq. units

(b) 4 $\mathrm{\pi }$ sq. units

(c) 6$\mathrm{\pi }$ sq. units

(d) 8$\mathrm{\pi }$ 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 and area of the circle will be.

Therefore, from the given condition we have,

………(1)

………(2)

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

Simplifying further we get,

Cancelling x we get,

Now we will cancel

………(3)

Now we will multiply both sides of the equation (3) by we get,

Therefore, area of the circle is.

Hence, option (b) is correct.