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Lesson 13.1 Skills Practice
Name ________________________________________________________ Date _________________________
Slicing and DicingSlicing Through a Cube
VocabularyDefine the term in your own words.
1. cross-section
Problem SetSketch a plane intersecting a cube such that the cross-section looks like each given
two-dimensional figure.
1.
Answers may vary.
2.
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3.
4.
5.
6.
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Name ________________________________________________________ Date _________________________
7.
8.
Describe the cross-section that results from the intersection of a plane and a cube as described
in each problem.
9. A plane intersects a cube perpendicular to its base. The plane bisects the base into
two congruent triangles.
The cross-section is a rectangle.
10. A plane intersects exactly three vertices of a cube.
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Lesson 13.1 Skills Practice page 4
11. A plane intersects a cube parallel to its base.
12. A plane intersects exactly three faces of a cube.
13. A plane intersects five faces of a cube, but does not intersect the sixth face.
14. A plane intersects a cube and is perpendicular to its base. The plane intersects two opposite
lateral faces of the cube, but is not perpendicular to any lateral faces.
15. A plane intersects every face of a cube.
16. A plane intersects two opposite vertices of the base, but is not perpendicular to the base.
The plane intersects two edges of the other base.
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Lesson 13.2 Skills Practice
Name ________________________________________________________ Date _________________________
The Right StuffSlicing Through Right Rectangular Prisms
Problem SetSketch a plane intersecting a right rectangular prism that is not a cube such that the cross-section
looks like each given two-dimensional figure.
1.
Answers may vary.
2.
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Lesson 13.2 Skills Practice page 2
3.
4.
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Lesson 13.2 Skills Practice page 3
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5.
6.
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7.
8.
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Lesson 13.2 Skills Practice page 5
Name ________________________________________________________ Date _________________________
Describe the cross-section that results from the intersection of a plane and a right rectangular prism as
described in each problem.
9. A plane intersects a right rectangular prism such that it only intersects three faces.
The cross-section is a triangle.
10. A plane intersects a right rectangular prism parallel to its square base.
11. A plane intersects a right rectangular prism parallel to its rectangular base.
12. A plane intersects exactly five faces of a right rectangular prism.
13. A plane intersects a right rectangular prism such that exactly one edge of the prism is in the plane.
14. A plane intersects a right rectangular prism such that it intersects all six faces.
15. A plane intersects two opposite vertices of the base, but is not perpendicular to the base.
The plane intersects two edges of the other base.
16. A plane intersects two opposite vertices of the base, but is not parallel to the base. The plane does
not intersect the other base.
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And Now On To PyramidsSlicing Through Right Rectangular Pyramids
VocabularyFill in each blank with the appropriate key term from the given word bank.
pyramid base lateralface lateraledge
vertex height regularpyramid slantheight
1. A is a polyhedron formed by connecting one polygonal face to several
triangular faces.
2. A is a pyramid in which the base is a regular polygon.
3.
Lesson 13.3 Skills Practice
Name ________________________________________________________ Date _________________________
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Lesson 13.3 Skills Practice page 2
Problem SetSketch a plane intersecting a right rectangular pyramid to achieve each stated goal.
1. Sketch a plane intersecting a square pyramid such that the cross-section looks like the
given square.
Answers may vary.
2. Sketch a plane intersecting a square pyramid such that the cross-section looks like the given
triangle. The plane should not pass through any of the vertices of the pyramid.
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Lesson 13.3 Skills Practice page 3
Name ________________________________________________________ Date _________________________
3. Sketch a plane intersecting a square pyramid such that the cross-section looks like the given
trapezoid. The plane should not pass through any of the vertices of the pyramid.
4. Sketch a plane intersecting a right rectangular pyramid that is not a square pyramid such that the
cross-section looks like the given rectangle.
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Lesson 13.3 Skills Practice page 4
5. Sketch a plane intersecting a square pyramid such that the cross-section looks like the
given triangle.
6. Sketch a plane intersecting a right rectangular pyramid that is not a square pyramid such that the
plane passes through the vertex and two opposite vertices of the base.
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Lesson 13.3 Skills Practice page 5
Name ________________________________________________________ Date _________________________
7. Sketch a plane intersecting a right rectangular pyramid that is not a square pyramid such that
the plane passes through two opposite vertices of the base and does not pass through the vertex.
8. Sketch a plane intersecting a square pyramid such that the plane passes through two consecutive
vertices of the base and does not pass through any other vertices of the pyramid.
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Lesson 13.3 Skills Practice page 6
Describe the cross-section that results from the intersection of a plane and a right rectangular pyramid
as described in each problem.
9. A plane intersects a square pyramid perpendicular to its base and passing through the vertex.
The cross-section is a triangle.
10. A plane intersects a square pyramid parallel to its base.
11. A plane intersects a right rectangular pyramid that is not a square pyramid parallel to its base.
12. A plane intersects a square pyramid perpendicular to its base, but does not pass through the
vertex. The plane is also parallel to two edges of the base.
13. A plane intersects a rectangular pyramid perpendicular to its base such that it intersects only two
lateral faces.
14. A plane intersects a right rectangular pyramid such that it passes through two consecutive vertices
of the base and does not pass through any other vertices in the pyramid.
15. A plane intersects a square pyramid such that it passes through the vertex and two opposite
vertices of the base.
16. A plane intersects a square pyramid such that it passes through all four lateral faces, is not parallel
to the base, and is parallel to two edges of the base.
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Lesson 13.4 Skills Practice
Name ________________________________________________________ Date _________________________
Backyard BarbequeIntroduction to Volume and Surface Area
VocabularyAnswer each problem.
1. Suppose you measured the amount of rice that would fit into a cube.
Using math terms, describe what the amount of rice in the cube represents. Explain your answer.
2. Use a real life example to describe surface area.
Problem SetCalculate the volume of the rectangular prism.
1.
8 in.
5 in.
2 in.
2.
1.5 cm3 cm
14 cm
V 5 (8) ? (2) ? (5)
V 5 80 in.3
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3.
8 m
3.5 m2 m
4.
8 m
13 m5 m
5.
4 in.
4 in.4 in.
6.
21 ft6 ft
9 ft
Describe how you would separate each solid to calculate the volume.
7.
Separate the solid into two rectangular
prisms – one prism is the bottom of the “L”,
and the other prism is the top of the “L”.
8.
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Lesson 13.4 Skills Practice page 3
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9. 10.
11. 12.
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Lesson 13.4 Skills Practice page 4
Calculate the volume of the solid formed by rectangular prisms.
13.
2 ft
1 ft
1 ft
3 ft
1 ft
14.
5 m
1 m
6 m
4 m
1 m
V 5 top prism 1 bottom prism
V 5 (1)(1)(1) 1 (4)(1)(1)
V 5 1 1 4
V 5 5 ft3
15. 2 cm 2 cm
1 cm
2 cm
2 cm
2 cm
6 cm
1 cm
6 cm
16.
6 yd
4 yd
1 yd
2 yd2 yd
2 yd
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Lesson 13.4 Skills Practice page 5
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17.
12 ft
2 ft
1 ft9 ft
1 ft 2 ft 18. 1 mm 1 mm
19 mm
15 mm1 mm
12 mm
Calculate the surface area of the rectangular prism.
19.
2 m
8 m
3 m
20.
1.5 in.9 in.
3 in.
SA 5 2lw 1 2lh 1 2wh
5 2(3)(2) 1 2(3)(8) 1 2(2)(8)
5 12 1 48 1 32
5 92 m2
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21.
4 cm
6 cm
11 cm
22.
23 m
12 m
5 m
23.
10 mm3 mm
9 mm
24.
12 yd
12 yd
3 yd
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Lesson 13.4 Skills Practice page 7
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Determine the number of polygonal surfaces each given solid has. Then describe the surfaces.
25.
There are 8 polygonal surfaces. Six surfaces
are lateral faces in the shapes of rectangles.
Two polygonal surfaces are bases that have
an “L” shape.
26.
27. 28.
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29. 30.
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Famous PyramidsApplying Volume and Surface Area Formulas
Problem SetCalculate the surface area of each square pyramid.
1.
8 in.
6 in.6 in.
SA52bs 1 b2
SA5 2(6)(8) 1 (6)2
SA5132 in2
Lesson 13.5 Skills Practice
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2.
18 ft
12 ft12 ft
3.
42 m
27 m27 m
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4.
20 m
15 m15 m
5.18 in.
18 in.18 in.
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6.20 yd
22 yd22 yd
7.
33 m
21 m21 m
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Lesson 13.5 Skills Practice page 5
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8.36 in.
40 in.40 in.
9.
75 cm
50 cm50 cm
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10.
300 ft
225 ft225 ft
Calculate the volume of the square pyramid.
11.
9 in.
10 in.10 in.
V51 __ 3
b2h
V51 __ 3
(10)2(9)
V5300 in3
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12.9 ft
12 ft12 ft
13.
11 cm
7 cm7 cm
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14.
20 m
25 m25 m
15.
22 ft
30 ft30 ft
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16.
28 mm
21 mm21 mm
17.
34.5 in.
42 in.42 in.
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18.75 cm
90 cm90 cm
19.
125 yd
100 yd100 yd
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20.
180 ft
200 ft200 ft
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