Question

Tick the correct answer in the following and justify your choice: if the perimeter and area of a circle are numerically equal, then the radius of circle is
A.2 units
B. \[\pi \]units
C.4 units
D.7 units

Answer 1

Hint: We know that the area of a circle with radius r is \[A=\pi {{r}^{2}}\]and perimeter of a circle with radius r is given by \[P=2\pi r\]and given area and perimeter of circle are numerically equal so, equating area of circle with radius r and perimeter of circle having radius r we will get the radius of required circle.

Complete step-by-step solution:
Given that perimeter of a circle and area of a circle are numerically equal
We know that the perimeter of the circle is given by formula,
\[P=2\pi r\]. . . . . . . . . . . . . . . . . . . (1)
We know that the area of the circle is given by the formula,
\[A=\pi {{r}^{2}}\]. . . . . . . . . . . . . . . . . . . . (2)
The perimeter of a circle and area of a circle are numerically equal
So, A=P
\[2\pi r=\pi {{r}^{2}}\]
\[\dfrac{2\pi }{\pi }=\dfrac{{{r}^{2}}}{r}\]
\[r=2\]units
So, the radius of circle obtained when perimeter of a circle and area of a circle are numerically equal is 2 units
So, the correct option for above question is option (A).

Note: we know that the circle is a collection of points where all points are equidistant from a given ‘O’. here point ‘O’ is called centre of circle. The distance from the centre of circle to any point on the circle is called radius and it is denoted by r. the line passing through the centre of the circle and touches the two points on the boundary of the circle is diameter and it is double the radius.