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
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 length x of the fourth side.
The function of the what?
The perimeter fence?
Let x = length of the rectangle
And y = width of the rectangle
x*y = 6000
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.