Multiple Choice. Each question is worth one point.
1. Use Euler’s Formula to find the missing number.
Vertices: 13
Edges: 28
Faces: ?
V+F=E+2
17
16
20
2. Describe the cross section.
How many sides are
on the cross section?
pentagon
trapezoid
hexagon
3. Find the lateral area and the surface area of the box to the nearest whole number.
LA = ph
SA = ph + 2(area of base)
95 cm2; 365 cm2
47 cm2; 365 cm2
95 cm2; 275 cm2
4. Use formulas to find the lateral area and surface area of the given prism. Round your answer
to the nearest whole number.
The base is the triangle
LA = (3+ 9 + 9.49)(37)
SA = LA + 2(1/2 *3*9)
795 m2; 809 m2
758 m2; 849 m2
795 m2; 822 m2
5. Find the surface area of the cylinder to the nearest whole number.
LA = 2 𝜋*r*h
SA = LA + 2𝜋*r2
1,659 in.2
898 in.2
5,862 in.2
6. Find the surface area of the pyramid shown to the nearest whole number.
770 m2
7. Find the surface area of a conical grain storage tank that has a height of 43 meters and a
diameter of 14 meters. Round the answer to the nearest square meter.
959 m2
SA = 𝜋(7)(43.6) +
𝜋(72)
1,113 m2
2,072 m2
8. Find the slant height of the cone to the nearest whole number.
92 + 172 = l2
21 m
19 m
17 m
9. The lateral area of a cone is 555
nearest tenth.
cm2. The radius is 37 cm. Find the slant height to the
15 cm
10. Find the lateral area and surface area of the cone. Round the answers to the nearest tenth. The
figure is not drawn to scale.
L.A. = 791.7 ft2; S.A. = 1,244.1 ft2
11. Find the lateral area of the cone to the nearest whole number.
LA = 𝜋* r * l
To find l : 302 + 402 = l2
Not drawn to scale
7,540 m2
4,712 m2
9,425 m2
12. Find the volume of the given prism. Round to the nearest tenth if necessary.
V = l*w*h
599.3 cm3
593.9 cm3
447.8 cm3
13. Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 5 yards by
5 yards by .83 yards for a patio if the concrete costs $46.00 per cubic yard?
V = l*w*h
$431.25
Total cost: V*cost per cubic yard
$2587.50
$95.83
14. Find the volume of the cylinder in terms of
.
𝑉 = 𝜋𝑟 2 ℎ
52.8 m3
58.08
m3
127.78
m3
15. Find the volume of the cylinder in terms of
. h = 6 and r = 3
𝑉 = 𝜋𝑟 2 ℎ
27
in.3
in.3
108
54
in.3
16. Find the height of the cylinder.
𝑉 = 𝜋𝑟 2 ℎ
2.4 in.
7.2 in.
14.4
17. Find the volume of the composite space figure to the nearest whole number.
180 cm
18. Find the volume of the square pyramid shown. Round to the nearest tenth if necessary.
V = 1/3 (area of base)(height)
147.7 cm3
44 cm3
528 cm3
19.Find the volume of the square pyramid shown. Round to the nearest tenth if necessary.
V = 1/3 (area of base)(height)
h = √202 − 122
9,216 ft3
192 ft3
3,072 ft3
20. A rectangular pyramid fits exactly on top of a rectangular prism. The prism has a length of 15
cm, a width of 5 cm, and a height of 7 cm. The pyramid has a height of 13 cm. Find the volume
of the composite space figure.
850 cm3
21. Two square pyramids have the same volume. For the first pyramid, the side length of the
base is 20 in. and the height is 21 in. The second pyramid has a height of 84 in. What is the side
length of the base of the second pyramid?
V = 1/3 (area of base)(height)
10 in.
Find volume of first pyramid
21 in.
Use that volume to find the
base length of the second
28 in.
22. Find the volume of a square pyramid with base edges of 40 cm and a slant height of 25 cm.
V = 1/3 (area of base)(height)
533.3 cm3
8,000 cm
h = √252 − 202
3
12,000 cm3
23. Find the surface area of the sphere with the given dimension. Leave your answer in terms of
.
radius of 70 m
SA = 4𝜋𝑟 2
4,900
m
m2
19,600
9,800
2
m2
24. Find the surface area of the sphere with the given dimension. Leave your answer in terms of
𝜋.
diameter of 10 cm
100
cm2
50
cm2
20
cm2
SA = 4𝜋𝑟 2
25. A balloon has a circumference of 19 cm. Use the circumference to approximate the surface
area of the balloon to the nearest square centimeter.
115 cm2
26. Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit.
𝑉=
4 3
𝜋𝑟
3
134 mm3
201 mm3
268 mm3
27. Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit.
𝑉=
4 3
𝜋𝑟
3
268 cm3
2,145 cm3
536 cm3
28. The volume of a sphere is 3,000
square meter?
2,158 m2
m3. What is the surface area of the sphere to the nearest
29. Are the two figures similar? If so, give the similarity ratio of the smaller figure to the larger
figure.
Compare
18
72
4
8
𝑎𝑛𝑑
𝑎𝑛𝑑
3
18
yes; 1 : 4
yes; 1 : 2
no
30. Are the two figures similar? If so, give the similarity ratio of the smaller figure to the larger
figure.
Compare
9.5
13.3
𝑎𝑛𝑑
1.8
2.52
yes; 1 : 2.4
yes; 1 : 1.4
yes; 1 : 1.2
31. Find the similarity ratio of a cube with volume 343 ft3 to a cube with volume 2,744 ft3.
49 : 196
Reduce:
3
√343
1:2
2:1
3
√2744
32. If the scale factor of two similar solids is 3 : 16, what is the ratio of their corresponding
areas? What is the ratio of their corresponding volumes?
Ratio of areas: a2:b2
The ratio of their corresponding areas is 3 : 256.
The ratio of their corresponding volumes is 3 : 4,096.
Ratio of volumes: a3:b3
The ratio of their corresponding areas is 27 : 4,096.
The ratio of their corresponding volumes is 9 : 256.
The ratio of their corresponding areas is 9 : 256.
The ratio of their corresponding volumes is 27 : 4,096.
33. The volumes of two similar solids are 729 m3 and 125 m3. The surface area of the larger solid
is 324 m3. What is the surface area of the smaller solid?
100 m2