Question

If the area of a circle is 78.5cm square, find its circumference.

Answer 1

Answer:

31.42 cm approx.

Step-by-step explanation:

$\text{Let the radius of the circle be r.}\\\\\text{Then. area = } \pi r^2\\\\\text{But, given area = 78.5 cm} ^2\\\\\text{Thus, according to the question,}\\\\pi r^2 = 78.5\\\\\implies \dfrac{22}{7} \times r^2 = \dfrac{785}{10}\\\\\\\implies r^2 = \dfrac{785 \times 7}{10 \times 22}\\\\\\\implies r^2 = 24.977\\\\\implies r = \sqrt{24.977} = \boxed{4.99 \: cm}$

$\text{circumference = } 2 \pi r\\\\= 2 \times \dfrac{22}{7} \times 5\\\\\\= 31.42 \: cm \: approx.$

Hope it helps.

Answer 2

Circumference = The boundary of the  circle

Area = The space occupied by the circle

Formula for circumference = $\bf2\pi r$ [ r = radius ]

Formula for area = $\bf\pi r^2$

$Area\: of\: circle = 78.5\:cm \\ \\ => \pi r^2  = \dfrac{785}{10} \\ \\=> \dfrac{22}{7}\times r^2 = \dfrac{785}{10} \\ \\ => r^2 = \dfrac{785}{10}\times\dfrac{7}{22}\\ \\ => r^2 = 24.997 \\ \\ r^2=\sqrt{24.118} \\ \\ r = \boxed{4.99\:cm}$

Now we know the radius of the circle, next step is to find the circumference

Circumference = $\bf2\pi r$

$=> 2\times3.14\times4.99$

$=> 31.3372$

Hope it helps you :)