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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
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