Question

Taking $ \pi = 3.14 $ , find the radius and circumference of a circle whose area is: $ 379.94{m^2} $ .

Answer 1

Hint: First we have to define what the terms we need to solve the problem are.
Since the radius is half of the diameter from any circle or cube or anything, that means diameter can be written as $ d = \dfrac{r}{2} $ and also radius can be remade as $ r = 2d $ .
In this problem, we just need to find the radius of the area of the circle and then we can find the circumference of the circle by using the radius and meter square given.
Formula used: Area of the circle is $ \pi {r^2} $ where r is the radius. Circumference of the circle is $ 2\pi r $ .

Complete step by step answer:
First, we have to find the value of the radius for a given circle; since the area of the circle is given as $ 379.94{m^2} $ (meter square), also in general we know that the area of the circle formula is $ \pi {r^2} $ .
So, combine the two same formulas and values from the given to get the value of the radius, hence equivalating we as an equation we get $ \pi {r^2} = 379.94{m^2} $ .
Now the value of the pie can be written as $ \pi = 3.14 $ , substitute the value of the pie in the above equation we get $ {r^2} = \dfrac{{379.94}}{\pi } \Rightarrow \dfrac{{379.94}}{{3.14}} $ .
Further solving by using the operator of the division we get $ {r^2} = 121 $ . Now we are going to take the square root on both sides; thus, we get $ r = \sqrt {121} \Rightarrow r = 11 $ , Hence the radius of the given problem is eleven meters (the root of the square meter is meter).
Applying the value of the radius in the circumference of the circle formula we get $ 2\pi r \Rightarrow 2(3.14) \times 11 $ further solving this by multiplication we get $ 69.08m $ .
Hence, we get the radius of the circle is $ r = 11 $ the meter and the circumference of the circle is $ 69.08m $ .

Note: we are also able to simplify the given problem by substituting the radius of the circle formula into the circumference of the circle and using the help of pie and $ 379.94{m^2} $ . Also, the square root of the meter square is meter, like applying the roots in numbers $ \sqrt {{m^2}} = m $ .