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Pre-Test
Name ________________________________________________________ Date _________________________
1. The figure shows one of the ways in which a cube can be sliced by a plane to form a
cross section.
Identify the shape of the cross section and describe how the cube was sliced.
2. The figure shows one of the ways in which a right rectangular prism that is not a cube can be
sliced by a plane to form a cross section.
Identify the shape of the cross section and describe how the prism was sliced.
3. Answer each question about square pyramids.
a. How many faces does a square pyramid have?
b. Describe the shapes of the faces of a square pyramid.
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c. What is the name of the point where all of the lateral faces intersect?
d. What is the name used to describe the altitude of the lateral faces?
4. A box has length 12 centimeters, width 7 centimeters, and height 5 centimeters.
a. Calculate the volume of the box. Show the formula you used.
b. Calculate the surface area of the box. Show the formula you used.
5. The figure shows a square pyramid.
25 m
30 m
20 m
a. Calculate the volume of the pyramid. Show the formula you used.
b. Calculate the surface of the pyramid. Show the formula you used.
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Post-Test
Name ________________________________________________________ Date _________________________
1. The figure shows one of the ways in which a cube can be sliced by a plane to form a cross section.
Identify the shape of the cross section and describe how the cube was sliced.
2. The figure shows one of the ways in which a right rectangular prism that is not a cube can be
sliced by a plane to form a cross section.
Identify the shape of the cross section and describe how the prism was sliced.
3. Answer each question about square pyramids.
a. How many lateral faces does a square pyramid have?
b. Describe the shapes of the lateral faces of a square pyramid.
c. What are the lateral edges of a square pyramid?
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d. What is the name used to describe the perpendicular from the apex of a pyramid to
the base?
4. A box has length 22 inches, width 11 inches, and height 15 inches.
a. Calculate the volume of the box. Show the formula you used.
b. Calculate the surface area of the box. Show the formula you used.
5. The figure shows a square pyramid.
39 ft
30 ft
36 ft
a. Calculate the volume of the pyramid. Show the formula you used.
b. Calculate the surface of the pyramid. Show the formula you used.
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Mid-ChapterTest
Name ________________________________________________________ Date _________________________
1. Is a cube a two-dimensional or three-dimensional figure?
2. Is a cross section a two-dimensional or three-dimensional figure?
3. How are cross sections of a cube formed?
4. How many faces does a cube have?
5. What shapes are the faces of a cube?
6. What cross section is formed by slicing through a cube in a direction parallel to any face?
7. What cross section is formed by slicing through a cube in a direction perpendicular to
any face?
8. How would all the cross sections formed by slicing through a cube in a direction parallel
to or perpendicular to a face be related to each other?
9. How would all the cross sections formed by slicing through a cube in a direction parallel
to or perpendicular to a face be related to the faces of the cube?
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10. Sketch a plane intersecting the cube shown such that the cross section forms a rectangle
that is not a square.
11. Sketch a plane intersecting the cube shown such that the cross section forms a triangle.
a. How can you ensure that the triangular cross section is an equilateral triangle?
b. Is it possible to create a circular cross section? Explain.
Mid-ChapterTest page 2
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Mid-ChapterTest page 3
Name ________________________________________________________ Date _________________________
Describe the cross section that you would obtain if you sliced through a cube in the way described.
12. The cube is sliced in a way such that the plane passes through five of the six faces of the cube.
13. The cube is sliced in a way such that the plane passes through three intersecting edges,
cutting off a corner of the cube.
14. The cube is sliced in such as way that the plane passes through all six faces of the cube.
15. The cube is sliced in a way such that the plane passes through the middle of the cube in
a direction perpendicular to the base.
16. The cube is sliced in a way such that the plane passes through two parallel edges,
where one edge is in the upper-left portion of the cube and the other edge is in the
lower-right portion of the cube.
17. How many faces does a right rectangular prism have?
18. What shapes are the faces of a right rectangular prism?
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19. Is a cube a right rectangular prism? Explain.
20. Does every right rectangular prism have any faces that are congruent?
21. Can a right rectangular prism have 6 square faces? Explain.
22. Can a right rectangular prism have exactly 4 square faces? Explain.
23. Can a right rectangular prism have exactly 2 square faces? Explain.
24. Can a right rectangular prism have no square faces?
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Mid-ChapterTest page 5
Name ________________________________________________________ Date _________________________
The figure shows a right rectangular prism that is not a cube, but which has two opposite faces
that are squares, and that are considered as the bases of the prism.
base
base
Describe how you could slice a right rectangular prism like this one to obtain each cross section.
25. a square
26. a rectangle that is not a square
27. a triangle
28. an equilateral triangle
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29. a pentagon
30. a hexagon
31. a parallelogram that is not a rectangle
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EndofChapterTest
Name ________________________________________________________ Date _________________________
1. List 5 different cross sections of a cube.
2. Is it possible to create an octagonal cross section of a cube? Explain.
3. Draw a plane perpendicular to the base that passes through the middle of the right
rectangular prism.
a. Describe the cross section formed as the plane passes through the solid.
b. Suppose the perpendicular plane does not pass through the middle of the rectangular
prism. Describe the cross section.
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4. The figure shows a square pyramid.
c.
a.d.
e.
f.
b.
Name each part of the pyramid to which the lettered arrows are pointing.
a.
b.
c.
d.
e.
f.
5. Draw a plane perpendicular to the base that passes through the middle of the square pyramid.
a. Describe the cross section formed as the plane passes through the pyramid.
b. Suppose that the perpendicular plane does not pass through the middle of the pyramid.
Describe the cross section.
EndofChapterTest page 2
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6. A box of individually wrapped snacks is shown.
10 in. 3.5 in.
6 in.
a. What is the shape of each side of the box?
b. What is the mathematical name for this solid figure?
c. Sketch each side of the box and include the measurements.
d. Calculate the volume of the box. Show the formula you used.
e. Calculate the surface area of the box. Show the formula you used.
EndofChapterTest page 3
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7. The diagram represents a brick oven.
2 ft
5 ft
6 ft
4 ft
2 ft1 ft
1 ft
Calculate the volume of the oven. Explain your reasoning.
8. The figure shows a square pyramid.
12 m
15 m
18 m
a. Calculate the volume of the pyramid. Show the formula you used.
b. Calculate the surface of the pyramid. Show the formula you used.
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1. How would you slice a right rectangular prism to create a pentagon?
a. Slice the prism such that the plane cuts through all of the six faces.
b. Slice the prism such that the plane cuts through three intersecting edges.
c. Slice the prism such that the plane is perpendicular to the base.
d. Slice the prism such that the plane cuts through five of the six faces.
2. How many 1-inch 3 1-inch 3 1-inch cubes could fit inside the cube shown, with no extra space?
16 in.
16 in.
16 in.
a. 96
b. 256
c. 1536
d. 4096
3. How would you slice through a cube such that the figure formed by the intersecting plane
is a rectangle that is not a square?
a. from the upper left edge of the cube to the lower right edge
b. perpendicular to the base
c. parallel to the base
d. passing through three intersecting edges
StandardizedTestPractice
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StandardizedTestPractice page 2
4. Which is the correct name for the part of the pyramid to which the arrow is pointing?
a. height
b. slant height
c. lateral edge
d. vertex
5. Suppose you slice through a square pyramid such that the plane is parallel to the base
and halfway up the total height of the pyramid. How does the side length of the cross section
compare to the side length of the base?
a. The side length of the cross section is 1 __ 4
the side length of the base.
b. The side length of the cross section is 1 __ 2
the side length of the base.
c. The side length of the cross section is the same as the side length of the base.
d. The side length of the cross section is 3 __ 4
the side length of the base.
6. Which formula gives the volume of a square pyramid, where b represents the length and width of
the square base and h represents the height of the pyramid?
a. V 5 1 __ 3
bh2
b. V 5 1 __ 2
b2h
c. V 5 1 __ 3
b2h
d. V 5 2s 1 b2
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7. Which solid figure is not a right rectangular prism?
a.
b.
c.
d.
8. How would you slice through a cube such that the figure formed by the intersecting
plane is a triangle?
a. from the upper left edge of the cube to the lower right edge
b. perpendicular to the base
c. parallel to the base
d. passing through three intersecting edges
9. The diagram represents a barbecue. What is the volume of the barbecue?
1 ft
1.25 ft
1.5 ft
6 ft
5 ft
4 ft
a. 120 cubic feet
b. 104.25 cubic feet
c. 20.25 cubic feet
d. 84 cubic feet
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10. Suppose you slice a square pyramid such that the plane just touches the vertex. What is
formed at the intersection of the plane and the pyramid?
a. a point
b. a square
c. a triangle
d. a quadrilateral
11. How much cardboard would you need to make a shipping carton with dimensions
12 inches 3 10 inches 3 7 inches?
a. 274 square inches
b. 548 square inches
c. 840 square inches
d. 840 cubic inches
12. What is the surface area of the square pyramid?
97.5 yards
75 yards75 yards
90 yards
a. 68,750 square yards
b. 5625 square yards
c. 14,625 square yards
d. 20,250 square yards
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13. Which best describes the cross section formed as the plane passes through the cube?
a. a square
b. a triangle
c. a parallelogram
d. a hexagon
14. One of Mollie’s favorite toys is a set of hollow rectangular plastic blocks that can be filled
with water to use as bath toys. The red block has dimensions 4 inches 3 6 inches 3 5 inches.
How much water will fill this block?
a. 148 square inches
b. 148 cubic inches
c. 120 cubic inches
d. 120 square inches
15. Suppose a plane passes through the center of a square pyramid perpendicular to the base. Which
two-dimensional figure is formed?
a. a circle
b. a rectangle
c. a square
d. a triangle
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16. What is the volume of the square pyramid?
34 feet
32 feet
30 feet
a. 2530 cubic feet
b. 10,240 cubic feet
c. 11,605.3 cubic feet
d. 30,720 cubic feet
17. Which cross section is formed when a cube is sliced in a way such that the plane passes through
the cube parallel to one of the bases?
a. a rectangle
b. a square
c. a triangle that is not equilateral
d. a parallelogram that is not a rectangle
18. Suppose a plane intersects a cube through three intersecting edges. How can you ensure
that the triangular cross section is an equilateral triangle?
a. The corner of the cube can be sliced off such that the three vertices of the triangle are at the
same distance from the corner of the cube.
b. The corner of the cube can be sliced off such that the two vertices of the triangle are at the
same distance from the corner of the cube.
c. The corner of the cube can be sliced off such that the plane intersects the base.
d. The corner of the cube can be sliced off such that the plane is perpendicular to the base.
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19. The two cross sections shown resulted from the intersection of two planes parallel to the base
of a solid. Which could be the solid?
Cross Section #1 Cross Section #2
a. a cube
b. a rectangular prism
c. a square pyramid
d. a sphere
20. Which figure cannot be made by slicing through a cube?
a. a square
b. an octagon
c. a triangle
d. a rectangle
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