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
choice
correct-choice
choice
choice
comment
10
16
20
22
24
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
choice
choice
correct-choice
choice
comment
11
12
13
14
15
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
choice
choice
comment
33
37
42
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
choice
correct-choice
choice
choice
comment
24
30
36
42
48
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
choice
choice
choice
correct-choice
comment
6
8
12
14
16
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
correct-choice
choice
choice
choice
comment
3
4
5
6
7
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
choice
choice
choice
comment
6
8
10
12
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
8