Posted by Elizabeth on Saturday, October 13, 2012 at 10:41pm.
A metal cylindrical container with an open top is to hold 1 cubic foot. If there is no waste in construction, find the dimensions which will require the least amount of material.
- Calculus - Reiny, Sunday, October 14, 2012 at 12:42am
V = πr^2 h
h = 1/(πr^2)
Surface Area (SA)
= bottom + collar of cylinder
= πr^2 + 2πrh
=πr^2 + 2πr(1/(πr^2)
= πr^2 + 2/r
dSA/dr = 2πr - 2/r^2 = 0 for a min of SA
2πr = 2/r^2
r^3 = 1/π
r = 1/π^(1/3) = appr .693 ft
then h = 1/(π(.693^2)) = .683
- Calculus - zeeshan amir khan, Sunday, January 12, 2014 at 8:01am
V = π r ² h = 1ft³
h = 1/π r ²
SA = π r ² + 2 π r h
= π r ² + 2 π r * 1/π r ²
= π r ² + 2 / r
SA ' = 2π r - 2 / r² = 0
2π r = 2 / r²
r³ = 1/π
r = 1/ ³√π ft
h = 1/(π r ²)
= 1/(π (1/ ³√π) ²)
= ³√π ² / π
= 1/ ³√π ft
Answer This Question
More Related Questions
- calculus - A cylindrical metal can with an open top is to be constructed. the ...
- Calculus - I actually have two questions: 4. An open box is to be made from a ...
- Calculus - A cylindrical metal can is made to hold 500ml of soup. Determine the ...
- Calc 1 (Optomization) - A rectangular storage container with an open top is to ...
- calculus - A cylindrical container is to hold 20π cm^3. The top and bottom ...
- math - A right cicular cylindrical can is to be constructed to have a volume of ...
- Calculus - A right cicular cylindrical can is to be constructed to have a volume...
- Math - A right circular cylinder is to be designed to hold 750 cm3 of processed ...
- math - A right circular cylinder is to be designed to hold 750 cm3 of processed...
- Calculus applications - A steel factory wishes to make a cylindrical container, ...