What are the dimensions of the lightest open-top right circular cylindrical can that will hold a volume of 125
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What are the dimensions of the lightest open-top right circular cylindrical can that will hold a volume of 125

[From: ] [author: ] [Date: 11-12-11] [Hit: ]
Then solve the derivative for dA = 0 which is the point where the slope of the derivative = 0 and is the minimum point of the curve.Then enter the value of r into the equation for volume to find h.......
With process please!

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There are two equations, one for weight and one for volume. weight is proposrtional to surface area of material; assuming that material is uniform thickness"

V = 125 = pi(r^2)h

A = pi(r^2) + 2pi(r)h

We can solve the first equation for 'h' (height) and substitute this in second equation to eliminate 'h' as a variable.

h = 125 / pi(r^2); substituting the right side for 'h' in second equation:

A = pi(r^2) + 2pi(r)[125 / pi(r^2)]
A = 3.14r^2 + 79.6r^-1

To find the minimum value of area, differentiate area with respect to radius (dA/dr). Then solve the derivative for dA = 0 which is the point where the slope of the derivative = 0 and is the minimum point of the curve. Then enter the value of 'r' into the equation for volume to find 'h'.
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