The dimensions of the can are radius of can = 4cm and
height of can = 78.6cm
What is the volume of cylinder?
A cylinder can be seen as a collection of multiple congruent disks, stacked one above the other. In order to calculate the space occupied by a cylinder, we calculate the space occupied by each disk and then add them up.
Thus, the volume of the cylinder can be given by the product of the area of base and height.
Volume of cylinder = πr²h
According to the given question:
We have V cylinder = V = 400cc
We will first find the areas involved
Let x = radius of base then area of the base = π*x² and this is the area of the top too
For lateral area we need to get h the height of the cylinder as function of x
V = πx²h ⇒ h= v/πx² ⇒ h = 400/πx²
Now the total area of the cylinder is:
A(x) = Area of the base + area of the top + lateral area
A(x) = 2*π*x² + 2πx h ⇒ A(x) = 2*π*x² + 2πx (V/πx² )
A(x) = 2*π*x² + 800/x
Taking derivatives:
A´(x) = 4πx - 800/x²
A´(x) = 0 4πx - 800/x² =0 ⇒ πx - 200/x² = 0
( πx³ - 200 )/ x² = 0
πx³ - 200 = 0
x = 4 cm
and h = 400/πx² ⇒ h = 78.6 cm
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