Question

If the area of a circle is 25 pi how do you find the length of the radius?

Answer 1

Hint: Here in this question, we have to find the radius of a circle. The radius of a circle is defined as the distance between the centre of the circle and outer region of a circle. It is given as \[A = \pi {r^2}\]. On substituting the values to the formula, we obtain the required result to the above question.

Complete step-by-step solution:
A circle is a shape consisting of all points in a plane that are a given distance from a given point or centre; equivalently it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant. The Radius is the distance from the centre to outwards. The Diameter goes straight across the circle, through the centre of a circle. The Circumference is the distance once around the circle.
The formula for the radius is given by \[A = \pi {r^2}\], where A is the area and r is the radius of a circle. As in the question they have mentioned the area. The radius of a circle is not given. By the definition of area of circle we simplify for the radius
Therefore the formula is
\[ \Rightarrow A = \pi {r^2}\]
The area is given as \[A = 25\pi square.units\], on substituting the value of A we have
\[ \Rightarrow 25\pi = \pi {r^2}\]
Cancelling the \[\pi \]on the both sides we get
\[ \Rightarrow 25 = {r^2}\]
Apply the square root on both sides
\[ \Rightarrow \sqrt {{r^2}} = \sqrt {25} \]
\[ \Rightarrow r = 5units.\]
Therefore the radius of a circle is 5 units.

Note: While finding area or circumference the unit must and should be mentioned in the final answer. Suppose if we don’t mention the unit then there is no value for the result at all. The unit for the circumference will remain the same as the unit mentioned for the radius or diameter. But the unit for the square is included.