Topic 1 Solid Geometry

Question 1 mode Multiple Choice name Shading on a cube text The large cube shown is made up of 27 identically sized smaller cubes. For each face of the large cube, the opposite face is shaded the same way. The total number of cubes that must have at least one face shaded is:

choice 10 choice 16 correct-choice 20 choice 22 choice 24 comment 1987 AMC 8 PROBLEM 7 % Question 2 mode Multiple Choice name Forming a number cube and adding up faces at a corner text The figure may be folded along the lines shown to form a number cube. Three number faces come together at each corner of the cube. What is the largest sum of three numbers whose faces come together at a corner?

1 choice 11 choice 12 choice 13 correct-choice 14 choice 15 comment 1989 AMC 8 PROBLEM 20. % Question 3 mode Multiple Choice name Painting cubes text An artist has 14 cubes, each with an edge of one meter. She stands them on the ground to form a sculpture as shown. She then paints the exposed surface of the sculpture. How many square meters does she paint?

choice 21 choice 24

2 correct-choice 33 choice 37 choice 42 comment 1989 AMC 8 PROBLEM 23 % Question 4 mode Multiple Choice name Chopping corners on a prism and counting edges text Each corner of a rectangular prism is cut off. Two (of the eight) cuts are shown. How many edges does the new figure have?

choice 24 choice 30 correct-choice 36 choice 42 choice 48 comment 1990 AMC 8 PROBLEM 18 % Question 5 mode Multiple Choice name Cutting a cube into smaller cubes text A cube of edge 3 centimeters is cut into N smaller cubes, not all the same size. If the edge of each of the smaller cubes is a whole number of centimeters, then N = choice 4 choice 8 choice 12 choice 16 correct-choice 20

3 comment 1991 AMC 8 PROBLEM 24 % Question 6 mode Multiple Choice name Folding pattern for cubes text Which pattern of identical squares could NOT be folded along the lines shown to form a cube? choice

choice

choice

4 correct-choice

choice

5 comment 1992 AMC 8 PROBLEM 20 % Question 7 mode Multiple Choice name Diagonals in a cube text A cube has eight vertices and 12 edges. A segment, such as x, which joins two vertices not joined by an edge is called a diagonal. Segment y is also a diagonal. How many diagonals does a cube have?

choice 6 choice 8 choice 12 choice 14 correct-choice 16 comment 1997 AMC 8 PROBLEM 17 % Question 8 mode Multiple Choice name Using cubes to form a side/front view text A figure is constructed from unit cubes. Each cube shares at least one face with another cube. What is the minimum number of cubes needed to build a figure with the front and side views shown?

6 choice 3 correct-choice 4 choice 5 choice 6 choice 7 comment 2003 AMC 8 PROBLEM 15 Question 9 mode Multiple Choice name Painting a block castle red text Fourteen white cubes are put together to form the figure illustrated. The complete surface of the figure, including the bottom, is painted red. The figure is then separated into individual cubes. How many of the cubes have exactly four red faces?

choice 4

7 correct-choice 6 choice 8 choice 10 choice 12 comment 2003 AMC 8 PROBLEM 13 Question 10 mode Multiple Choice name Volume of a dual to a cube text Centers of adjacent faces of a unit cube are joined to form a regular octahedron. What is the volume of this octahedron? Hint: the volume of a pyramid is Bh/3, where B is the area of the base, and h is the height of the pyramid. Find the side length of the octahedron. choice 1/8 correct-choice 1/6 choice 1/4 choice 1/3 choice 1/2 comment 2006 AMC 10 A, Problem 24

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