1. ## Function problems

I have 2 word problems that I am having trouble with:

The surface area of a cylindrical can of radius r and height h is
2pi r squared + 2pi r h. If the can is twice as high as the diameter of its top, express its suface areqa S as a function of r.

and:

A rectanular region of 6000 square feet is to be fenced in on three sides with fencing that costs $3.75 per foot and on the fourth side with fencing that costs$2.00 per foot.

a. Express the cost of the as a function a function of the length x of the fourth side.

b. Find the domain of the function.

Any help would be greatly appreciated.

2. The surface area of a cylindrical can of radius r and height h is
2pi r squared + 2pi r h. If the can is twice as high as the diameter of its top, express its suface areqa S as a function of r.

The diameter of the top (and of the bottom too) is 2r
So the h will be 2(diameter) = 2(2r) = 4r
Then,
A = 2pi(r^2) +2pi(r)(4r)
A = 2pi(r^2) +8pi(r^2)
A = 10pi(r^2)

In function form,

A rectanular region of 6000 square feet is to be fenced in on three sides with fencing that costs $3.75 per foot and on the fourth side with fencing that costs$2.00 per foot.

a. Express the cost of the as a function a function of the length x of the fourth side.

The function of the what?
The perimeter fence?

Okay.

Let x = length of the rectangle
And y = width of the rectangle

x*y = 6000
So,
y = 6000/x

Cost of perimeter fence, C = (x +2y)(3.75) +x(2.00)
C(x) = (x +2(6000/x))(3.75) +2x
C(x) = 3.75x +45,000/x +2x