?The length l, width w, and height h of a box change with time. At a certain instant the
Chapter 12, Problem 43(choose chapter or problem)
The length l, width w, and height h of a box change with time. At a certain instant the dimensions are \(l=1 \mathrm{m}\) and \(w=h=2 m\), and l and w are increasing at a rate of \(2 \mathrm{m} / \mathrm{s}\) while h is decreasing at a rate of \(3 \mathrm{m} / \mathrm{s}\). At that instant find the rates at which the following quantities are changing.
(a) The volume
(b) The surface area
(c) The length of a diagonal
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