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'.
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'.