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)`