(Solved): The length , width w, and height h of a box change with time. At a certain instant the dimension ...

The length $?$, width $w$, and height $h$ of a box change with time. At a certain instant the dimensions are $?=3\mathrm{m}$ and $w=h=2\mathrm{m}$, and $?$ and $w$ are increasing at a rate of $5\mathrm{m}/\mathrm{s}$ while $h$ is decreasing at a rate of $8\mathrm{m}/\mathrm{s}$. At that instant find the rates at which the following quantities are changing. (a) The volume. * ${\mathrm{m}}^3/\mathrm{s}$ (b) The surface area. * ${\mathrm{m}}^2/\mathrm{s}$ (c) The length of a diagonal. (Round your answer to two decimal places.) * $\mathrm{m}/\mathrm{s}$