Question

How do you find the radius of a circle with an area of $ 80\text{ c}{{\text{m}}^{2}} $ ?

Answer 1

Hint: We express the general expressions for a circle. We use the radius as r and the area of that circle with radius r as $ \pi {{r}^{2}} $ . We equate the value $ \pi {{r}^{2}} $ , with the given value of $ 80\text{ c}{{\text{m}}^{2}} $ and find the value of r.

Complete step by step answer:
Let us assume the radius of a circle is r units.
We also know that the area of the circle with the radius r will be $ \pi {{r}^{2}} $ square units.
Now, it is given that for a circle the area value of the circle is $ 80\text{ c}{{\text{m}}^{2}} $ .
This gives the equality of $ \pi {{r}^{2}}=80 $ . We have a quadratic equation of r. We solve it to find the value of r. we first find the value of $ \pi {{r}^{2}} $ by dividing with $ \pi $ .
We take the value of $ \pi $ as $ 3.14 $ and solve the equation.
 $ \begin{align}
  & \pi {{r}^{2}}=80 \\
 & \Rightarrow {{r}^{2}}=\dfrac{80}{\pi }=25.46 \\
\end{align} $
Now we take the square root on the both sides of the equation $ {{r}^{2}}=25.46 $ .
The square root gives
 $ \begin{align}
  & {{r}^{2}}=25.46 \\
 & \Rightarrow r=\sqrt{25.46}=5.05 \\
\end{align} $ .
This value is the approximate value of the radius.

The diameter of the circle will be double of the radius.
So, the diameter is $ 2r=2\times 5.05=10.1 $ .
Therefore, the radius of a circle with area $ 80\text{ c}{{\text{m}}^{2}} $ is $ 5.05\text{ cm} $ .

Note:
 We have been asked to find the radius. The value of the radius can never be negative. That’s why at the time of finding the root value we neglected the negative root value. Every quadratic equation has two roots with equal value but opposite sign.