Question

How do you find the circumference and the area of the circle whose equation is \[{{x}^{2}}+{{y}^{2}}=36\]?

Answer 1

Hint: In this problem, we have to find the area of the circle whose equation is \[{{x}^{2}}+{{y}^{2}}=36\]. We know that the formula for the area of the circle is \[\pi {{r}^{2}}\], which contains the radius in it. We also know the general equation of the circle. We can compare the general equation of the circle and the given equation, to find the value of the radius to substitute in the area formula, to find the area value.

Complete step by step solution:
We know that the given equation of the circle is,
\[{{x}^{2}}+{{y}^{2}}=36\] ……. (1)
We also know that the general equation of the circle is,
\[{{x}^{2}}+{{y}^{2}}={{r}^{2}}\] …….. (2)
Where r is the radius of the circle.
We can now compare the equation (1) and the equation (2), we get
\[\begin{align}
  & \Rightarrow {{r}^{2}}=36 \\
 & \Rightarrow r=6 \\
\end{align}\]
The value of the radius is 6.
We know that the formula for the area of the circle is,
Area of the circle is = \[\pi {{r}^{2}}\]units
Area of the circle is = \[3.14\times {{6}^{2}}\]= \[3.14\times 36=113.04\]units.
Therefore, the area of the circle is 113.04 units.

Note: Students make mistakes while finding the radius from the equation. We should remember that the constant term r in the equation is the radius. We should also know some geometric formulas to be used in these types of problems. Students make mistakes while writing the units, in which we should concentrate.