Let the height be h, and the radius r
V = pir^2h
900 = pir^2h
h = 900/(pir^2)
For the surface area I am including 2 circles,
SA = 2pir^2 + 2pi(r)(h)
= 2pir^2 + 2pir(900/pir^2)
= 2pir^2 + 1800/r
d(SA)/dr = 4pir - 1800/r^2 = 0 for a min of SA
4pir = 1800/r^2
r^3 = (1800/(4pi)
r = 5.2
yes, you are right, so proceed with the largest value of r allowed, r = 5
then h = 900/(25pi) = 11.459 which is within the given restriction.
Plug in those values in my SA equation.
The radius of a tank can not exceed 5m, and the height can not exceed 12 m. Is it possible to construct a tank with a volume of 900m^3? If it is possible, determine the minimum amount of material required to make the tank.
When i solve it, the radius exceeds the restrictions.. so i believe that it is not possible. Can someone verify this?
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1 answer