1. A box without a top is to be made from a rectangular piece of cardboard, with dimensions 8 in. by 10 in., by cutting out square corners with side length x and folding up the sides. l8 in.i 10 in. (a) Write an equation for the volume Vof the box in terms of x. (b) Use technology to estimate the value of x, to the nearest tenth. that gives the greatest volume. Explain your process. 2. A cube-shaped aquarium has edges that are 3 ft long. The aquarium is lled with water that has a density of 62 lb/ft3. (a) Should the aquarium be placed on a table that can support a maximum weight of 200 lb? Explain why or why not. (b) Would the density of the water change if the aquarium was only half full? Explain. Answer: 3. Use the Fermi process to estimate the number of bricks needed to ll an empty bathtub. Assume a typical brick has a length of 4 inches, a width of 2 inches and a height of 8 inches. A typical bathtub has a length of 60 inches, a height of 30 inches and a width of 18 inches. Show your work