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Q.

why we use π for finding the area of a circle and choose the correct formula for area of circle when r is radius.

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a

π * (Radius)

b

π * (Radius)^{3}

c

π * (Radius)^{1 / 2}

d

π * (Radius)^{2}

answer is D.

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Detailed Solution

Due to the curved shape of the circle, it is challenging to determine a specific dimension.
It has been noted that a circle's area and circumference depend on its diameter.
In circle ratio of the circumference and the diameter was observed to be similar but not equal.
Aryabhata defined irregularity of the ratio as an irrational number.
Then he found a value for the ratio which is up to five significant as pi.
i.e.π= (Circumference)/ (Diameter)
Hence,
Circumference=π∗Diameter
=π∗2 (Radius)
And also, Area= (Circumference/2) ∗Radius
=π (Radius) ∗Radius

= π * (Radius)^{2}

Correct option is 4.

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