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

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8 π

sq. units

6 π

sq. units

2 π

sq. units

4 π

sq. units

answer is A.

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Detailed Solution

Given that, and circumference of circle are numerically equal.
Let

x

represents the area of the circle so the circumference is also be equal to

x

2 π r = x ......... (1)

π r 2 = x .............. 2

Solve the equation (1) to determine the value of r.

r = x 2 π

Substitute the value of r into the equation (2) to determine the area of the circle.

π x 2 π 2 = x

⇒ π . x 2 4 π 2 = x

Solve the equation for

x

x = 4 π

The area is represented by

4 π

square units.
Therefore, the area is represented by

4 π

square units.
Hence the correct option is 1.

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