Question

The formula for the area of a circle is A = r 2. Classify the area of a circle with a radius of 0.75 centimeters as either rational or irrational.

Answer 1

area of circle , $A\propto r^2$
e.g., A = kr² , here k is proportionality constant and value of k = π { an irrational number}
so, area of circle , A = πr²

now according to question,
radius of circle , r =0.75 cm = 3/4 cm { a rational number}
so, area of circle , A = π (3/4)² = 9π/16 cm² {an irrational number }

as you know, rational × irrational = irrational number
hence, area of circle is an irrational number.