If the side of a square is equal to the diameter of a circle, what is the area of the square if the area of the circle is 81π sq. cm?

324 sq cm

The area of a circle is given by the formula:

$\text{Area of circle} = \pi r^2$

Given that the area of the circle is $81\pi\text{ sq. cm}$:

$\pi r^2 = 81\pi$

$r^2 = 81$

$r = 9\text{ cm}$

The diameter ($d$) of the circle is twice the radius:

$d = 2 \times 9 = 18\text{ cm}$

We are given that the side of the square ($s$) is equal to the diameter of the circle:

$s = 18\text{ cm}$

The area of a square is calculated as:

$\text{Area of square} = s^2 = 18^2 = 324\text{ sq. cm}$