Find the area of the circle whose circumference is 154 cm sq.

Given: Circumference of the circle is 154 cm sq

To do: Find the area of the circle.

Solution:

Formula to find the Area of a circle  =  π$r^2$

π  =  constant ;  r  =  radius  

We can find the radius from the circumference, which is 154 sq cm.

Circumference of circle  =  $2πr$

S, by equating the formula of the circumference and given   circumference,

$2πr  =  154$ 

$2  \times  \frac{22}{7}\times  r  =  154$        [π =$ \frac{22}{7}$ always]

$r  = 154 \times \frac{ 7}{ 2} \times 22$   [to find r, keep r in one side and number in other side]

 

$r = \frac{7 \times 7}{  2}$                            [$7 \times 22 = 154$]

$r = \frac{49}{ 2}$ cm

Now,  the Area of a circle  =  π$r^2$

 

                                               =  $\frac{22}{7}\times \frac{49}{2} \times \frac{49}{2}$

                                               = $\frac{11 \times 7 \times 49}{2}$  [$11\times 2 =22 ;  7 \times 7= 49$]

                                               = $\frac{3773}{ 2}$

 

                                               =  $1886.5$ sq cm 

Area of circle is  1886.5 sq cm