Math Graded Assignment Extended Problems: Reasoning

Math | Graded Assignment | Extended Problems: Reasoning

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Graded Assignment

Extended Problems: Reasoning

Answer the questions. When you have finished, submit this assignment to your Learning Coach.

(4 points)

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1. A slice is being made to a cube. For each description—

· 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

(d) a slice that contains the midpoint of , the midpoint , and vertex F

Answer:

(4 points)

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2. Two friends have clay models of square pyramids. They are describing slices that they are making to the square pyramid.

(a) Leani makes a slice that results in a square. What slice did Leani make?

(b) Tierra makes a slice that also results in a square but it is smaller. Explain how this could have happened.

(c) Tierra and Leani both make slices to their square pyramids that result in a triangle. However, their triangles are not similar. Describe the girls’ possible slices.

(d) Leani says she plans to make a slice that will result in a rectangle by making a slice through 1 of the triangle faces so that the cut is parallel to the edge of the base as shown below. Tierra tells Leani that the slice would not result in a rectangle. Do you agree with Tierra? Explain why or why not.

Answer:

(8 points)

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3. Beverly needs to make a container in the shape of a rectangular prism that holds 1000 in3 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.

Answer:

(4 points)

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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’s 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.

Answer:

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