SOLUTION: This is an optimization problem.
The problem states that a cylinder has a volume of 1000 cubic inches; therefore, what dimensions will minimize the surface area?
The conflict
Algebra ->
Volume
-> SOLUTION: This is an optimization problem.
The problem states that a cylinder has a volume of 1000 cubic inches; therefore, what dimensions will minimize the surface area?
The conflict
Log On
Question 1061644: This is an optimization problem.
The problem states that a cylinder has a volume of 1000 cubic inches; therefore, what dimensions will minimize the surface area?
The conflict is that the answer I have doesn't match the teacher's answer.
Here's what I did:
V = (pi) * (r^2) * h
1000 = (pi) * (r^2) * h
1000 / ((pi) * (r^2)) = h
SA = 2 * ( (pi) * r^2 ) + (2 * (pi) * r * h)
SA = 2 * ( (pi) * r^2 + (pi) * r * ( 1000 / ((pi) * (r^2)) )
SA = 2 * ( (pi) * r^2 + 1000/r )
SA = 2 * (pi) * r^2 + 2000/r
SA' = 4 * (pi) * r - 2000/(r^2)
0 = 4 * (pi) * r - 2000/(r^2)
4 * (pi) * r = 2000/(r^2)
4 * (pi) * r^3 = 2000
r^3 = 500 / (pi)
r = root3 ( 500 / (pi) )
The problem is that r is supposed to be equal to root3 ( 250 / (p) ).
Where did I go wrong? Answer by solver91311(24713) (Show Source):
You did not go wrong. The radius that gives the minimum total surface area is .
cannot possibly be the answer because that radius value yields a surface area that is roughly 28 square inches larger than the surface area of the cylinder with the inch radius.
John
My calculator said it, I believe it, that settles it
