Additional Practice
ACTIVITY 4.1
1. Determine whether the net can be cut out
and folded to form a cube.
2. Draw two nets made of six squares that will
form a cube and two that will not.
3. What is the surface area of a cube that has
side lengths of 5 cm?
4. What is the edge length of a cube that has a
surface area of 1350 cm2?
5. Calculate the surface area and volume of the
prism below.
UNIT 4
7. Mariah is filling a terrarium with sand for
1 of the
her tarantula. The sand will only be __
4
way to the top. If the length of the terrarium
is 17 inches, the width 12 inches, and the
height 12 inches, what is the volume of the
sand she is using?
8. The Gray family is putting in a pool. The
first plan shows a pool that is 15 feet long,
12 feet wide, and 5 feet deep. The second
plan shows the same length and width, but
shows a depth of 7 feet. How much more
water will be needed to fill the second pool if
both pools are filled to the top?
9. How many cubes with a side length of
3 inches will fit into the rectangular prism
below? Explain.
6 in.
12 in.
30 in.
ACTIVITY 4.2
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10. Use this cube to answer parts a–d below.
23 in.
N
M
O
8 in.
P
11 in.
Q
6. To mail a box of treats to her sister in
college, Courtney needs the box she sends
to have a volume of less than 56 in.3 The box
she is considering sending has a length of
8 inches, a width of 4 inches, and a height of
3 inches. Should she use this box? Explain.
R
S
T
a. Name two skew line segments.
b. Name two parallel line segments.
c. What is the intersection of planes NPTR,
MNRQ, and QRTS?
d. What is the intersection of planes QRTS
and MOSQ?
Level 2, Unit 4 • Three-Dimensional Geometry
1
UNIT 4
Additional Practice
11. Use the top, side, and front views to sketch
the solid.
Top View
Side View
16. Find the volume of each solid and put the
volumes in order from greatest to least.
Front View
8m
5m
18 m
12 m
18 m
6m
17 m
12. Sketch the front, side, and top views of the
solid shown below.
17. Find the volume of the triangular prism.
13 cm
16.5 cm
15 cm
13. Sketch the top, bottom, and side views of a
triangular prism.
14. Sketch an octagonal prism.
18. Find the volume of this cone.
15. Determine the volume of the figure sketched
on the dot paper. The edge of each cube
represents one unit.
7.75 in.
12 in.
19. The Great Pyramid of Giza, a square
pyramid, has decreased in size over time.
Currently, its height is approximately
137.2 meters and the length of each side of
the base is approximately 230 meters. What
is its volume? Round to the nearest tenth.
2
SpringBoard® Mathematics with MeaningTM Level 2
© 2010 College Board. All rights reserved.
ACTIVITY 4.3
Additional Practice
20. If the radius of the base of a cone is 9 ft and
the volume of the cone is 2543.4 f t3, what is
the height of the cone?
24. Determine the surface area of a regular
pentagonal prism with a base of area
580.5 in.2, a base edge length of 18 in. and
a height of 3.5 in.
25. Find the surface area of a regular triangular
pyramid with the dimensions shown below.
13 mm
21. Calculate the volume of the complex solid.
UNIT 4
9
6.
8 cm
14.5 mm
12 mm
14.5 mm
ACTIVITY 4.4
© 2010 College Board. All rights reserved.
22. The surface area of a cube is 216 square
inches. What is the length of an edge of the
cube?
23. Find the surface area of the triangular prism
whose base is equilateral.
13 cm
16.5 cm
15 cm
cm
26. Find the surface area of a soup can with
1 inches and a height of
a radius of 2__
2
1 inches. Leave your answer in terms of pi.
4__
4
27. A waffle cone has a slant height of 7 inches.
3 of a circle. What is its surface
The cone is __
4
area? Round to the nearest tenth. (Hint: A
waffle cone does not have a base so that you
can fill it with ice cream or yogurt.)
ACTIVITY 4.5
28. The side length of a square is tripled.
a. What will happen to the perimeter?
b. What will happen to the area?
29. The radius of a circle is doubled.
a. What will happen to the circumference?
b. What will happen to the area?
Level 2, Unit 4 • Three-Dimensional Geometry
3
UNIT 4
Additional Practice
30. A baseball field has baselines that are 90 feet
each. If a softball field, which has 60-ft
baselines, is drawn inside the baseball field,
by how much does the area of the baseball
field decrease to form the softball field?
31. The ratio of the areas of two circles is 1:4.
What is the ratio of the circumferences?
32. Each edge of a cube is 10 cm. The length of
each edge is multiplied by five.
a. What will happen to the surface area?
b. What will happen to the volume?
34. The radius of a sphere is multiplied by three.
a. What will happen to the surface area?
b. What will happen to the volume?
35. The surface areas of two similar triangular
pyramids 144 in.2 and 324 in.2
a. What is the ratio of the heights?
b. What is the ratio of the volumes?
c. If the volume of the smaller pyramid is
72 in.3, what is the volume of the larger
pyramid?
© 2010 College Board. All rights reserved.
33. The ratio of the radii of two spheres is 2:3.
If the radius of the smaller sphere is 8 cm,
what is the volume of the larger sphere?
Round to the nearest tenth.
4
SpringBoard® Mathematics with MeaningTM Level 2