Question

if the circumference of a circle is 2pi metres what is the area

Answer 1

Given :-

The circumference of a circle is $\sf 2 \pi$ metres

To Find :-

Area of the circle

Solution :-

We knows that , for a circle with Radius $\sf r$ units , the circumference and Area is given by :-

• Circumference = $\sf 2\pi r$ units

• Area = $\sf \pi r²$ sq. unit

Therefore , In the case of the question we have

Let us assume that ;

• Radius of given circle = $\sf r$ m

Now , According to question ;

$\quad \leadsto \quad \sf 2 \pi r = 2 \pi$

${ : \implies \quad \sf \cancel{2 \pi } r = \cancel{2 \pi}}$

${ : \implies \quad \bf r = 1 \: m }$

Now , Area of circle ;

$\quad \leadsto \quad \sf \pi r²$

${ : \implies \quad \sf \pi \times 1²}$

${ : \implies \quad \sf \pi \times 1 }$

${ : \implies \quad \bf \pi \; m² }$

$\quad \qquad { \bigstar { \underline { \boxed { \pmb { \bf { \red { \underbrace { \therefore Area \: of \: Circle \: = \: \pi \: m²}}}}}}}}{\bigstar}\quad \qquad$