9. (Related Rate Problem. You are designing tiles for the heat shield on the next generation...
9. (Related Rate Problem. You are designing tiles for the heat shield on the next generation of space shuttle. The tiles will have a box-like shape, where the width is equal to the height and the length is triple the width. Show your work for the following. A. Express the volume of the tile as a function of the width of the tile. 1 x V = volume = length x width x height = 3x B. These tiles heat up and expand during re-entry. If the dimensions of the tiles expand too much, the tiles will buckle against each other and allow the extreme heat to enter the shuttle. Based on the type of material used, the volume of the tile is expected to expand at a rate of 0.8 cm per second. Find the rate at which the width of the tile is expanding if the width is 8 cm.