SOLUTION: Could you assist me in solving a problem please? I can solve every problem in Chapter 2 of my daughter’s college algebra book except one and its bothering me. The surface area "S"

Algebra ->  Volume -> SOLUTION: Could you assist me in solving a problem please? I can solve every problem in Chapter 2 of my daughter’s college algebra book except one and its bothering me. The surface area "S"       Log On


   

Question 1027528: Could you assist me in solving a problem please? I can solve every problem in Chapter 2 of my daughter’s college algebra book except one and its bothering me. The surface area "S" of a right circular cylinder is given by the formula "S" = 2πrh + 2πr^2. If the height is twice the radius, find each of the following: a) A function S(r) for the surface area as a function of r. b) A function S(h) for the surface area as a function of h. That's it. When I solve for h in the original equation its equal to -r in order to plug it back into the Volume formula to solve for V(r). How can h be equal to -r and 2r as suggested in the word problem? I am missing something and I simply don't know what it is. Thank you.

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
system%28S=2%2Api%2Arh%2B2%2Api%2Ar%5E2%2Ch=2r%29
THE SECOND EQUATION IS IN THE PROBLEM DESCRIPTION!!


(a) Find the function S(r), surface area as a function or r.
SUBSTITUTE FOR h ACCORDING TO THE PROBLEM DESCRIPTION:
S%28r%29=2%2Api%2Ar%282r%29%2B2%2Api%2Ar%5E2 through substitution;
S%28r%29=2%2A2%2Api%2Ar%2Ar%5E2%2B2%2Api%2Ar%5E2
highlight%28S%28r%29=4%2Api%2Ar%5E3%2B2%2Api%2Ar%5E2%29


(b) Find surface area as a function of cylinder height, h.
-
h=2r
h%2F2=2r%2F2
h%2F2=r
-
Substitute for h in S.
S%28h%29=2%2Api%28h%2F2%29%2Ah%2B2%2Api%2A%28h%2F2%29%5E2
S%28h%29=2%2Api%2Ah%2Ah%2F2%2B2%2Api%2Ah%5E2%2F%282%2A2%29
highlight%28S%28h%29=pi%2Ah%5E2%2B%28pi%2Ah%5E2%29%2F2%29