Geometry Problem Set | Reference Guide Unit 7 | Surface Area and Volume of Pyramids
Surface Area and Volume of Pyramids
Problem Set
For each pyramid, identify the variable that represents each of the following:
A. Height
B. Slant height
C. Side length of base
3.
1.
a
e
d
y
z
w
b
c
v
x
2.
k
n
j
p
m
Answer the question.
4. Use the labeled square pyramid to write an
expression for each measure.
s
q
t
p
r
A. What is the volume of the pyramid?
B. What is the surface area of the pyramid?
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Geometry Problem Set | Reference Guide Unit 7 | Surface Area and Volume of Pyramids
Identify the vertex, base edges, lateral edges, and altitude of each pyramid.
5.
6.
A
A
H
I
D
B
E
F
C
G
J
F
C
D
B
E
Find the slant height of each pyramid.
7.
8.
24 km
16 cm
36 km
24 cm
Find the surface area of each regular pyramid.
9.
10.
10.77 m
10 m
8m
14.4 km
14 km
10.4 km
12 km
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Geometry Problem Set | Reference Guide Unit 7 | Surface Area and Volume of Pyramids
11.
14.
32 ft
22.09 km
33.6 ft
22 km
10.4 ft
12 ft
4 km
15.
12.
30 m
30.55 m
18 mi
17.32 m
12 mi
20 m
16.
13.
12 cm
20 m
14.8 cm
8.66 cm
10 cm
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14 m
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Geometry Problem Set | Reference Guide Unit 7 | Surface Area and Volume of Pyramids
17.
18.
A
14 cm
I
H
B
G
F
C
D
4.8 cm
E
8 yd
4 cm
height = 18 yd
Find the volume of each pyramid.
19. The figure is a square pyramid.
21. The figure is a square pyramid.
14 cm
20 cm
16.4 cm
12 cm
14 cm
20. The base of the triangular pyramid is equilateral.
22. The figure is a regular hexagonal pyramid.
26 km
22 km
18 m
13.9 km
16 km
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15.6 m
height = 34 m
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Geometry Problem Set | Reference Guide Unit 7 | Surface Area and Volume of Pyramids
23. The figure is a square pyramid.
26. The figure is a rectangular pyramid.
18 in.
17 m
8m
6m
15 in.
24. The base is a regular octagon.
27. The figure is a square pyramid.
6 cm
8.2 cm
8 cm
28. The figure is a regular octagonal pyramid.
10 cm
34 cm
12.07 cm
25. The base is a right triangle.
40 km
18.1 km
15 km
22 km
12 km
9 km
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Geometry Problem Set | Reference Guide Unit 7 | Surface Area and Volume of Pyramids
29. The figure is an oblique square pyramid.
30. The base is a regular pentagon.
18 m
8m
40 cm
height
5.5 m
24 cm
Answer each question.
31. What is the surface area to volume ratio of the
regular hexagonal pyramid shown here?
32. The main entrance to the Louvre Museum in
Paris, France, is a square pyramid made entirely
of glass. One side of the base is 35 meters and the
height is 20.6 meters.
20.6 m
9 in.
height = 28 in.
35 m
A. What is the surface area of the Louvre
Pyramid including its base?
B. What is the volume of the space occupied by
the Louvre Pyramid?
C. The area of a pane of glass in the Louvre
Pyramid is about 3 square meters. If the base
is excluded, about how many panes does the
pyramid have?
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Geometry Problem Set | Reference Guide Unit 7 | Surface Area and Volume of Pyramids
33. The Khafre Pyramid is one of the pyramids of the
Giza complex in Egypt. When it was originally
constructed, the base of the square pyramid was
704 feet on one side and 446 feet tall.
446 ft
704 ft
A. What was the surface area of the Khafre
Pyramid, including its base?
B. What was the volume of the Khafre Pyramid?
C. If the density of the rock used to build the
pyramid is 169 pounds per cubic foot, what is
the weight of the Khafre Pyramid?
35. Damian’s construction company is tiling the roof
of a gazebo. The roof is in the shape of a regular
hexagonal pyramid with an open bottom. The
side lengths of the hexagonal base are 5 feet and
the slant height is 7 feet.
A. Explain why the surface area of the
roof will not equal the surface area of a
regular hexagonal pyramid with the same
dimensions.
B. Calculate the volume and surface area of
the roof.
C. Explain which calculation from Part B
Damian would use to determine the number
of tiles he needs.
34. The dormer shown here is constructed by
combining a right triangular prism with an
oblique triangular pyramid. Find the volume of
the space the dormer occupies.
2 ft
5 ft
3 ft
3 ft
3 ft
5 ft
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