The surface area of a cylindrical can of radiusrand heighthis

2pi rsquared + 2pi r h.If the can is twice as high as the diameter of its top, express its suface areqaSas a function ofr.

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(r) = 10pi*r^2 --------------------------answer

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 lengthxof 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

C(x) = 5.75x +(45,000/x) -----------------answer.

b.Find the domain of the function.

Domain is what will give C(x) positive real value.

So, domain is from just after zero up to infinity. Or x > 0 ----answer.