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Remember the steps:Form an equation 
Find the minimum surface area of a cuboids (box) which has a square end, and a volume of 800cm^{3} 

Steps: 

1) Find an equation for surface area 
A = 2x^{2} + 4xL 
We only want one variable so eliminate L using the volume equation 

2) Volume equation  rearrange to be L = 
V = Lx^{2} 
3) Substitute L = 800/x^{2} back into the Area Equation 
A = 2x^{2} + 4xL 
4) Differentiate the Area equation 
A = 2x^{2} + 3200x^{1} 
5) Make the derivative = 0 and solve for x 
0 = 4x  3200x^{2} 
6) Calculate the surface area 
A = 2x^{2} + 3200/x 
Find the minimum surface area of a cylinder which has a volume of 330cm^{3} What are the dimensions of the cylinder? 
How does this look?Why are tin cans not this shape?But are like this? 

Steps: 

1) Find an equation for surface area 
2 circles + rectangle 

We only want one variable so eliminate L using the volume equation 

2) Volume equation  rearrange to be L = 
V = пr^{2}L 

3) Substitute L = 330/2пr^{2} back into the Area Equation 
A = 2пr^{2} + 2пrL 

4) Differentiate the Area equation 
A = 2пr^{2} + 660r^{1} 

5) Make the derivative = 0 and solve for r 
0 = 4 пr  660r^{2} 

6) Calculate the surface area 
A = 2п3.745^{2} + 660/3.745 

Dimensions 


Radius 
r = 5.5cm (1dp) 

Length 
L = 330/пr^{2} 