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Answer:
a) 18 in x 18 in x 18 in
b)
Step-by-step explanation:
a) Let's call 's' the side of the square base and 'h' the height of the solid.
The surface area is given by the equation:
The volume of the solid is given by the equation:
From the volume equation, we have that:
Then, using this value of h in the surface area equation, we have:
To find the side length that gives the minimum surface area, we can find where the derivative of S in relation to s is zero:
The height of the solid is:
b) The minimum surface area is: