Question

If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
(A) \[2\] units
(B) $\pi $ units
(C) $4$units
(D) $7$units

Answer 1

Hint:For a circle having radius $r$,the perimeter of the circle is given by \[2\pi r\] and the area of the circle is given by $\pi {r^2}$.Equating both equations we get the value of radius.

Complete step-by-step answer:
Perimeter or Circumference of the circle is the measurement of the boundary of the circle. If we open a circle and make a straight line out of it, then its length is the circumference.
Area of the circle is the region enclosed by the circle itself or the space covered by the circle. The formula to find the area of the circle is; $A = \pi {r^2}$, where $r$ is the radius of the circle.
According to the question,
Perimeter of the circle=Area of the circle
Perimeter of the circle=$2\pi r$
Area of the circle=$\pi {r^2}$
Now equating both we get,
Perimeter of the circle=Area of the circle
$ \Rightarrow $$2\pi r$=$\pi {r^2}$
Simplifying it we get,
$ \Rightarrow $$\dfrac{{2\pi }}{\pi } = \dfrac{{{r^2}}}{r}$
$ \Rightarrow $$r = 2$cm
The radius of the circle is given as $2cm$ if perimeter and area of circle area numerical.

So, the correct answer is “Option A”.

Note:We can also calculate in terms of diameter i.e Area of the circle=$\pi {\dfrac{d^2}{4}}$ and Perimeter of the circle=$\pi d$.Equating both and simplifying we get $d=4$ and it can be written as $2r =4$, we get $r=2cm$ which is same answer. Students should know the definitions and properties of circle.Also should remember the formulas of area and perimeter of circle for solving the types of questions.