Determine The Dimensions (length, Width, Height) With The Smallest Possible Surface Area. Use Lagrange Multipliers To Solve. Determine the dimensions (length, width, height) with the smallest possible surface area. Use Lagrange multipliers to solve.
When the tank is partially filled with water, a solid cube with an edge length of 1 foot is placed in the tank. If no overflow of water from the tank is assumed, by how many inches with the level of the water in the tank rise when the cube becomes completely submerged?
What are the dimensions of the tank that require the least material to build? (In other words, minimize the surface area.) Let x and y be the dimensions of the rectangular bottom. Then its area is xy.
