1. A slice is being made to a cube. For each slice—
• Describe the two-dimensional figure resulting from the described slice. Use the specific name when possible.
• Determine whether a different slice can produce a congruent two-dimensional figure. If so, describe or sketch an example of the slice. If not, explain why not.

(a) a slice parallel to the base
(b) a slice that contains and
(c) a slice that contains and vertex F


(Score for Question 2: ___ of 3 points)
2. Determine whether each statement is true or false. Justify each answer with a sketch of the cross section if the statement is true or a sketch of a counterexample if it is false.
(a) Every cross section of a rectangular prism is a rectangle.
(b) Every cross section of a cube is a square.



(Score for Question 3: ___ of 6 points)
3. Beverly needs to make a container in the shape of a rectangular prism that holds of liquid. The height of the container must be 10 in. She wants to use the dimensions that will allow her to use the least amount of material possible. Beverly’s mother says the difference in the amount of material will be too minor to worry about. Beverly believes it is possible to save more than half the material needed if they pick the right dimensions. Who is correct? Support your answer with specific numbers, and explain your reasoning. The dimensions are measured in whole units.


(Score for Question 4: ___ of 3 points)
4. Rodayna is making a huge cake in the shape of a house. The cake is a square prism with a pyramid on top. Rodayna made enough batter for 10,000 in3 of cake and enough frosting to frost 3000 in2 of cake. Does she have enough frosting and batter to make this cake? (She does not frost the bottom of the cake.) The formula for the volume of a right pyramid is , where B is the area of the base and h is the distance from the center of the base of the pyramid to its vertex.