Question

a designer wants to make a circular fountain inside a square of grass as shown at the right. What is a rule for the area A of the grass as a function of r?

Answer 1

Area of square = l*w
Area of circle = pi*r^2

Area of grass = (l*w) - (pi*r^2)

Answer 2

see the attached figure to better understand the problem

we know that

the area of a square is equal to

$A=b^{2}$

where

b is the length side of the square

in this problem, the length side of the square is equal to the diameter of the circle

so

b=2r

substitute in the formula of the area of the square

$A=(2r)^{2}$

$A=4r^{2}\ units^{2}$

Find the area of the circle

the area of the circle is equal to

$A=\pi r^{2}\ units^{2}$

Find the area of the grass

the area of the grass is the area of the square minus the area of the circle

so

$A=4r^{2} - \pi r^{2} = r^{2}*[4-\pi ]$

therefore

the answer is

the area A of the grass as a function of r is equal to

$A=r^{2}*[4-\pi ]\ units^{2}$