Question

How do you find the radius of a circle if its area is $254.5$ square inches?

Answer 1

Hint: We will use the formula for finding the area of a circle. Then, we will equate this formula to the area given in the problem. Then we will transpose accordingly to find the radius. The formula for finding the area of a circle is given by $A=\pi {{r}^{2}}$ where $A$ is the area and $r$ is the radius of the circle.

Complete step by step answer:
Let us consider the given problem.
We are asked to find the radius of a circle if its area is $254.5$ square inches.
Let us recall the formula we have learnt for finding the area of a circle whose radius is $r.$
So, the area of a circle $A=\pi {{r}^{2}}.$
Now, we can use this formula to find the radius $r$ by equating the given area.
So, we have $A=254.5$ square inches.
When we equate this value with the value in the formula, we will get $\pi {{r}^{2}}=254.5$ square inches.
Let us transpose $\pi $ from the left-hand side to the right-hand side.
We will get ${{r}^{2}}=\dfrac{254.5}{3.141}.$
Now, we have obtained an equation to find the value of ${{r}^{2}}.$
To find the value of $r,$ what we need to do is to find the square root of the whole equation.
We will get, $r=\sqrt{\dfrac{254.5}{\pi }}.$
We know that the value of $\pi =3.141.$
So, we will get $r=\sqrt{\dfrac{254.5}{3.141}}.$
By simple calculation, we will get $\dfrac{254.5}{3.141}=81.0252.$
So, we will get $r=\sqrt{81.0252}.$
We can find the square root on the RHS to get the radius, $r=9.0014$ square inches.

Hence the radius of the circle if its area is $254.5$ square inches is $r=9.0014$ square inches.

Note: The radius is approximately equal to $9$ square inches. Suppose that we are given with the circumference of the circle instead of the area. Then also, we will be able to find the radius $r$ of the circle using the formula $C=2\pi r.$