Question: 1. A box without a top is to be made from a rectangular piece of cardboard, with the dimensions shown below, by cutting out square

1. A box without a top is to be made from a rectangular piece of cardboard, with the dimensions shown below, by cutting out square corners with side length x and folding up the sides. fv-9 cm- (a) Write an equation for the volume of the box in terms of x. (b) Use technology (such as Desmos) to estimate the value of x, to the nearest tenth, that gives the greatest volume. Explain your process. 2. Aright cylinder-shaped vase is filled with decorative colorful sand. The image below displays the dimensions of the vase, and the decorative sand has a density of 1.52 g/cm3. 16 cm (a) Is it safe to place the vase on a shelf that can support a maximum weight of 2000 grams? Explain why or why not and show all your work. (b) Would the density of the sand change if the vase was only half full? Explain. 3. A marble making company is trying to estimate how many marbles they can fit in one of their shipping boxes. Each marble is a sphere with the dimensions shown below, and the shipping box is a rectangular prism with the dimensions shown below. Use the Fermi process to estimate the number of marbles that will fit in one shipping box. Show all your work. (Images not drawn to scale). 920 mm /560 mm 1700 mm '

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