A landscaper plants circular flower beds in square plots of land of various sizes. Once the flower bed is built, she fills in the uncovered land with sod (represented by the white region in the figure below). As a result, the amount of sod needed is determined by the size of the flower bed, which depends on the size of the square plot of land she uses.

A square measures x feet on each side. Within the square, a circle of radius r is centered at the center of the square. The circle just touches the square at the midpoint of each of the square's sides. The circle is shaded grey, while the remainder of the inside of the square is colored white.

Write an expression to determine the length of the side of the square, x , in terms of the circle's radius, r .

x

2r Correct

Define a function h that determines the area of the square plot in terms of the radius of the circular flower bed, r .

h(r) = 4r^2 Correct

Define a function k to determine the area of the circular flower bed in terms of its radius, r .

k(r) =pi r^2 Correct

Use function notation to determine the number of square feet of sod needed to fill in the white region above. (Hint: Use the functions for the area of the square plot, h , and the area of the circular flower bed, k .)

Incorrect

Using the function rules for h and k , define a function g that determines the number of square feet of sod (needed to fill in the white region above) in terms of the radius r of the circular flower bed.

g(r)=(4-pi) r^2 Correct