Question

How do you find the area of circle \[{x^2} + {y^2} = 25\]?

Answer 1

Hint: Area of circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, \[A = \pi {r^2}.\], where r is the radius of the circle.
From the given equation, comparing with the general equation at first, we will find the radius of the circle.
Then, applying the formula we can find the area of the circle.

Complete step-by-step solution:
It is given that; the equation of the circle is \[{x^2} + {y^2} = 25\].
We have to find the area of the given circle.
We know that the general equation of the circle with centre at the origin and radius \[r\] is \[{x^2} + {y^2} = {r^2}\].
So, the area of circle \[\pi {r^2}.\]
Comparing with the general equation, we get, the radius is \[r = 5\].
So, the area of the circle \[{x^2} + {y^2} = 25\] is \[\pi {5^2} = 25\pi \]

Hence, the area of the circle is \[25\pi \].

Note: Any geometrical shape has its own area. This area is the region occupied by the shape in a two-dimensional plane. So, the area covered by one complete cycle of the radius of the circle on a two-dimensional plane is the area of that circle.
Area of circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, \[A = \pi {r^2}.\], where r is the radius of the circle.
The general equation of the circle with centre \[(h,k)\] and the radius \[r\] is \[{(x - h)^2} + {(y - k)^2} = {r^2}\]. When the centre is at origin, the equation will be \[{x^2} + {y^2} = {r^2}\].