Geo - CH10 Practice Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Classify the figure. Name the vertices, edges, and base.
____
a. triangular pyramid
vertices: A, B, C, D, F
edges: AB, AC, AD, BC
base: triangle ABC
b. triangular pyramid
vertices: A, B, C, D, F
edges: AB, AC, AD, AF, FB, BC, CD, DF
base: rectangle DCBF
c. rectangular pyramid
vertices: A, B, C, D, F
edges: AB, AC, AD, BC
base: rectangle DCBF
d. rectangular pyramid
vertices: A, B, C, D, F
edges: AB, AC, AD, AF, FB, BC, CD, DF
base: rectangle DCBF
2. Describe the cross section.
____
____
a. The cross section is a circle.
c. The cross section is a plane.
b. The cross section is a cylinder.
d. The cross section is a parallelogram.
3. Find the drawing that represents the given object. Assume there are no hidden cubes.
a.
c.
b.
d.
4. Graph a rectangular prism with length 5 units, width 3 units, height 3 units, and one vertex at (0, –
5, 0).
a.
c.
b.
d.
____
____
____
____
5. Find the distance between the points (11, 6, 12) and (12, 7, 17). Round to the nearest tenth.
a. 39.2 units
c. 5.2 units
b. 3.0 units
d. 1.3 units
6. Find the lateral area and surface area of the right cylinder. Give your answer in terms of π.
a. lateral area: 30π m2;
c. lateral area: 30π m2;
2
2
surface area: 132π m
surface area: 69π m
b. lateral area: 78π m2;
d. lateral area: = 60π m2;
2
2
surface area: = 60π m
surface area: 78π m
7. Find the lateral area and surface area of a regular square pyramid with base edge length 6 m and
slant height 8 m.
a. lateral area: 132 m2;
c. lateral area: 132 m2;
2
2
surface area: 96 m
surface area: 48 m
b. lateral area: 96 m2;
d. lateral area: 48 m2;
2
2
surface area: 132 m
surface area: 132 m
8. Find the surface area of the composite figure. Round to the nearest square centimeter.
____
____
____
a. 550 cm2
c. 725 cm2
2
b. 656 cm
d. 814 cm2
9. Find the volume of a right rectangular prism with length 12 in., width 10 in., and height 6 in.
Round to the nearest tenth, if necessary.
a. 240 in2
c. 2,400 in3
b. 720 in3
d. 360 in3
10. Find the volume of the composite figure. Round to the nearest hundredth.
a. 28.26 ft3
c. 113.04 ft3
3
b. 84.78 ft
d. 197.82 ft3
11. Find the volume of a sphere with diameter 30 ft. Give your answer in terms of π.
a. 36, 000π ft3
c. 40π ft3
3
b. 4,500π ft
d. 2,250π ft3
Numeric Response
12. Find the surface area in square inches of a cylinder with a radius of 7 inches and a height of 4
inches. Use 3.14 for π. Round to the nearest tenth.
3
13. Find the height in centimeters of a square pyramid with a volume of
cm and a base edge
72
length equal to the height.
Matching
Match each vocabulary term with its definition.
a. cross section
b. edge
c. area
d. volume
e. vertex
f. perimeter
g. surface area
h. altitude
i. face
____
____
____
____
____
____
14. the number of nonoverlapping unit cubes of a given size that will exactly fill the interior of a threedimensional figure
15. the intersection of a three-dimensional figure and a plane
16. a perpendicular segment joining the base of a figure to the opposite vertex or parallel surface
17. a flat surface of the polyhedron
18. the total area of all faces and curved surfaces of a three-dimensional figure
19. a segment that is the intersection of two faces of the figure
Match each vocabulary term with its definition.
a. altitude of a pyramid
b. edge of a pyramid
c. vertex of a pyramid
d. base of a pyramid
e. oblique prism
f. right prism
g. regular pyramid
h. slant height of a regular pyramid
____
____
____
____
20.
21.
22.
23.
a prism whose lateral faces are all rectangles
the point opposite the base of the pyramid
the distance from the vertex of a regular pyramid to the midpoint of an edge of the base
a prism that has at least one nonrectangular lateral face
Geo - CH10 Practice Test
Answer Section
MULTIPLE CHOICE
1. ANS: D
All edges converge at the top of the figure, indicating that the figure is a pyramid. The base of the
pyramid is the rectangle DCBF. Therefore, the shape is a rectangular pyramid. The vertices are A,
B, C, D, and F. The indicated lines, including dashed lines, represent the edges:
AB, AC, AD, AF, FB, BC, CD, DF.
Feedback
A
B
C
D
The type of pyramid relates to the shape of its base.
The type of pyramid relates to the shape of its base.
Dashed lines create a three dimensional effect, but indicate edges as well.
Correct!
PTS: 1
DIF: Basic
REF: Page 655
OBJ: 10-1.1 Classifying Three-Dimensional Figures
NAT: 12.3.1.c
TOP: 10-1 Solid Geometry
2. ANS: A
The cross section is the intersection of the cylinder and the plane. The cross section is a circle.
Feedback
A
B
C
D
Correct!
The cross section is two dimensional.
The cross section is the intersection of the plane and the cylinder.
The cross section is the intersection of the plane and the cylinder.
PTS: 1
DIF: Basic
REF: Page 656
OBJ: 10-1.3 Describing Cross Sections of Three-Dimensional Figures
NAT: 12.3.4.c
TOP: 10-1 Solid Geometry
3. ANS: A
Rotate the object around the left column boxes 180°.
becomes
Feedback
A
B
C
D
Correct!
Try rotating the drawing about the left column of boxes.
Try rotating the drawing about the left column of boxes.
Try rotating the drawing about the left column of boxes.
PTS: 1
DIF: Average
REF: Page 664
OBJ: 10-2.4 Relating Different Representations of an Object
NAT: 12.3.1.d
TOP: 10-2 Representations of Three-Dimensional Figures
4. ANS: C
There are several different correct answers, only one of which is shown. The prism could be
entirely below the xy-plane, in front of (rather than behind) the yz-plane, or (0, –5, 0) could be on
the right-hand side (rather than the left-hand side) of the prism.
If (0, –5, 0) is chosen as the bottom, front, left-hand side vertex, the other vertices should be at (0,
0, 0), (0, –5, 3), (0, 0, 3), (–3, 0, 0), (–3, 0, 3), (–3, –5, 0), (–3, –5, 3).
Feedback
A
B
C
D
The height of the prism is 3 units.
The length of the prism is 5 units, not 8 units.
Correct!
The height of the prism is 3 units.
PTS:
OBJ:
TOP:
5. ANS:
d=
=
1
DIF: Average
REF: Page 671
10-3.3 Graphing Figures in Three Dimensions
10-3 Formulas in Three Dimensions
C
(x2 − x1)2 + (y2 − y1)2 + (z2 − z1)2 =
1 + 1 + 25 =
(12 − 11)2 + (7 − 6)2 + (17 − 12)2
27 ≈ 5.2 units
Feedback
A
B
C
D
Add the squared difference of the coordinates.
Take the square root of the sum of the difference of squares.
Correct!
Add the squared difference of the z-coordinates as well.
PTS: 1
DIF: Average
REF: Page 672
OBJ: 10-3.4 Finding Distances and Midpoints in Three Dimensions
TOP: 10-3 Formulas in Three Dimensions
6. ANS: D
Step 1 Find the lateral area for the cylinder.
Lateral area of a cylinder
L = 2πrh
= 2π(3)(10)
Substitute.
2
Simplify.
= 60π m
Step 2 Find the surface area for the cylinder.
Surface area of a cylinder
S = L + 2πr2
2
Substitute.
= 60π + 2π(3)
Simplify.
= 78π m2
Feedback
A
B
C
D
Multiply the lateral area by 2.
First, find the lateral area. Then, use the result to find the surface area.
First, find the lateral area. Then, use the result to find the surface area.
Correct!
PTS: 1
DIF: Average
REF: Page 682
OBJ: 10-4.2 Finding Lateral Areas and Surface Areas of Right Cylinders
NAT: 12.3.1.b
TOP: 10-4 Surface Area of Prisms and Cylinders
7. ANS: B
Step 1 Find the perimeter P.
A regular square pyramid has 4 base edges.
P = 4 ⋅ 6 = 24 m
Step 2 Find the lateral area.
L = 12 Pl
Lateral area of a regular pyramid
= 12 (24)(8)
= 96 m2
Substitute 24 for P and 8 for l.
Simplify.
Step 2 Find the surface area.
S = 12 Pl + B
Surface area of a regular pyramid
= 96 + 36
= 132 m2
2
Substitute 96 for 12 Pl. B = 6 = 36.
Simplify.
Feedback
A
B
C
D
The lateral area should be less than the surface area.
Correct!
The lateral area should be less than the surface area.
First, find the lateral area. Then, use the result to find the surface area.
PTS: 1
DIF: Basic
REF: Page 689
OBJ: 10-5.1 Finding Lateral Area and Surface Area of Pyramids
NAT: 12.2.1.j
TOP: 10-5 Surface Area of Pyramids and Cones
8. ANS: C
The height of the cone is 25 − 15 = 10 cm.
The slant height (l) of the cone is given by the Pythagorean Theorem,
l=
52 + 102 =
125 = 5 5 .
The lateral area of the cone is L = πrl = π( 5 ) ÊÁÁ 5 5 ˆ˜˜ = 25 5 π cm2.
Ë
¯
2
The lateral area of the cylinder is L = 2πrh = 2π(5)(15) = 150π cm .
2
2
2
The base area of the cylinder is B = πr = π(5) = 25π cm .
S = (cone lateral area) + (cylinder lateral area) + (base area)
= πÊÁÁ 25 5 + 150 + 25 ˆ˜˜ ≈ 725 cm2.
Ë
¯
Feedback
A
B
C
D
Include the lateral area of the cylinder.
Include the base area.
Correct!
The figure has just one base.
PTS:
OBJ:
NAT:
9. ANS:
1
DIF: Average
REF: Page 692
10-5.4 Finding Surface Area of Composite Three-Dimensional Figures
12.2.1.j
TOP: 10-5 Surface Area of Pyramids and Cones
B
Volume of a right rectangular prism
V = lwh
V = (12)(10)(6) = 720 in3
Substitute 12 for l, 10 for w, and 6 for h.
Feedback
A
B
C
D
The volume of a right rectangular prism is equal to the product of its length,
width, and height, and is expressed in cubic units.
Correct!
The volume of a right rectangular prism is equal to the product of its length,
width, and height.
The prism has a rectangular base.
PTS: 1
DIF: Basic
REF: Page 697
OBJ: 10-6.1 Finding Volumes of Prisms NAT: 12.2.1.j
TOP: 10-6 Volume of Prisms and Cylinders
10. ANS: C
2
2
3
The volume of the cylinder is V = πr h = π(3) (3) = 27π ft .
The volume of the cone is V = 13 πr2h = 13 π(3)2(3) = 9π ft3.
The volume of the water tank is the sum of the volumes.
V = (cylinder volume) + (cone volume)
= 27π ft3 + 9π ft3 = 36π ft3 ≈ 36 × 3.14 = 113.04 ft3.
Feedback
A
B
C
D
Add the volume of the cone to the volume of the cylinder.
Add the volume of the cone to the volume of the cylinder.
Correct!
The height of the cylinder is 3 ft, not 6 ft.
PTS:
OBJ:
NAT:
11. ANS:
1
DIF: Average
REF: Page 708
10-7.5 Finding Volumes of Composite Three-Dimensional Figures
12.2.1.j
TOP: 10-7 Volume of Pyramids and Cones
B
πr3
Volume of a sphere
V = 43
V = 43 π153
V = 4, 500π
Substitute 15 for r.
Simplify.
Feedback
A
B
C
D
The volume of a sphere is equal to 4/3 times pi, times the radius raised to the
third power.
Correct!
The volume of a sphere is equal to 4/3 times pi, times the radius raised to the
third power.
The volume of a sphere is equal to 4/3 times pi, times the radius raised to the
third power.
PTS: 1
DIF: Basic
REF: Page 714
OBJ: 10-8.1 Finding Volumes of Spheres
TOP: 10-8 Spheres
NAT: 12.2.1.j
NUMERIC RESPONSE
12. ANS: 483.6
PTS: 1
DIF: Average
NAT: 12.2.1.j
TOP: 10-4 Surface Area of Prisms and Cylinders
13. ANS: 6
PTS: 1
DIF: Advanced
NAT: 12.2.1.j
TOP: 10-7 Volume of Pyramids and Cones
MATCHING
14. ANS:
TOP:
15. ANS:
TOP:
16. ANS:
TOP:
17. ANS:
TOP:
D
PTS: 1
DIF:
10-6 Volume of Prisms and Cylinders
A
PTS: 1
DIF:
10-1 Solid Geometry
H
PTS: 1
DIF:
10-4 Surface Area of Prisms and Cylinders
I
PTS: 1
DIF:
10-1 Solid Geometry
Basic
REF: Page 697
Basic
REF: Page 656
Basic
REF: Page 680
Basic
REF: Page 654
18. ANS:
TOP:
19. ANS:
TOP:
G
PTS: 1
DIF: Basic
10-4 Surface Area of Prisms and Cylinders
B
PTS: 1
DIF: Basic
10-1 Solid Geometry
REF: Page 680
20. ANS:
TOP:
21. ANS:
TOP:
22. ANS:
TOP:
23. ANS:
TOP:
F
PTS: 1
DIF:
10-4 Surface Area of Prisms and Cylinders
C
PTS: 1
DIF:
10-5 Surface Area of Pyramids and Cones
H
PTS: 1
DIF:
10-5 Surface Area of Pyramids and Cones
E
PTS: 1
DIF:
10-4 Surface Area of Prisms and Cylinders
Basic
REF: Page 680
Basic
REF: Page 689
Basic
REF: Page 689
Basic
REF: Page 680
REF: Page 654