Name ______
Date ______
Cereal boxes come in different shapes and sizes. Some are tall and skinny, while others are shorter or deeper. The Bravo Breakfast cereal company is considering changing the size of its box. The staff members need some data to help them make the best choice.
The company currently packages its Morning Math Crunch cereal in a box that is 2" deep by 4" wide by 8" tall, as pictured at right. This shape is called a right rectangular prism because the top and bottom faces are rectangles that are congruent (same size and shape) and parallel to each other. These are called the bases. The other faces (sides of the box) are also rectangles that are perpendicular (at a right angle) to the bases. Use a set of cubes to build a model of this box. Assume that the edge of one cube represents 1" of length on the real cereal box. Check in the box when you have done this.
The cardboard sides of the box are called its faces. How much cardboard is needed to create all six of the faces of the box? Work with your team to develop a method for calculating this amount. Discuss the kind of units to use. Explain your method below. Go ahead and calculate the amount of cardboard required.
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The number of square units that it takes to cover the outside of an object, like the amount of cardboard you found in part (b), is called the object’s surface area. The volume of a shape is the measure of how much it will hold. Volume is measured in cubic units. How many cubes did you use to make this model of the cereal box? How many cubic inches of cereal will the box hold? ______
The waste-management division at Bravo Breakfast is worried that the box for Morning Math Crunch uses too much cardboard. The waste-management crew wantsto make a box that holds the same amount of cereal but uses less cardboard.
What measurement of the box is the waste-management division interested in minimizing (making as small as possible)? What measurement does the company want to keep the same? What could change? ______
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With your team, use the cubes to build different rectangular prisms that will still hold 64 cubic inches of cereal. Each box must be a rectangular prism with exactly six faces. For each prism you create:
---Sketch the prism,
---Label the dimensions on your sketch, and
---Find the surface area. How many different prisms can you make? ______
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Do all of the prisms you built have the same volume? How do you know?_____
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Which box will use the smallest amount of cardboard? ______
Use cubes to build each prism below. Find the surface area and volume of each shape.
c. Use at least 15 cubes to build a prism of your own design. Sketch the prism and find its surface area and volume.