Name:
Class:
Date:
Unit 11 PC Form D
1.
Use pencil and paper to answer the question.
Complete each sentence with one of the following names of the geometric solids.
cylinder
rectangular prism
cone
pyrmaid
a. I have a square base and I have exactly 5 vertices. I am a ____________________.
b. I have one base and exactly one vertex. I am a ____________________.
c. I have two bases and four faces. I am a ____________________.
d. I have exactly two bases and no vertices. I am a ____________________.
ANSWER:
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a. pyramid
b. cone
c. rectangular prism
d. cylinder
Page 1
Name:
Class:
Date:
Unit 11 PC Form D
2.
Use pencil and paper to answer the question.
a. Which of the boxes below has the greatest volume? ________
b. Explain how you know.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
ANSWER:
a. Box A
b. Sample answer: To get the volume of each prism, I multiplied the area of the base by
the height.
Box A has the greatest volume.
(Note: the first 2 numbers that are multiplied in the sample answer above
to show how the volume is found for each box are the dimensions for
the area of the base in the formula V
h.)
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Page 2
Name:
Class:
Date:
Unit 11 PC Form D
3.
Use pencil and paper to answer the question.
The rectangular prism below has a volume of 350
.
What is its height?
(unit)
ANSWER:
4.
10 in
Use pencil and paper to answer the question.
The rectangular prism below has a volume of 200
.
What is the area of the base?
(unit)
ANSWER:
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40 in
Page 3
Name:
Class:
Date:
Unit 11 PC Form D
5.
Use pencil and paper to answer the question.
Circumference of a circle: C =
d
Answer the following questions.
For part c, use the key on your calculator or use 3.14 as an approximation for
Round your answer to the nearest hundredth.
.
a. What is the radius of the circle?
__________________
b. What is the diameter of the circle?
__________________
c. What is the circumference of the circle?
__________________
ANSWER:
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a. 5 units
b. 10 units
c. 31.40 units (using 3.14), or 31.42 units (using
)
Page 4
Name:
Class:
Date:
Unit 11 PC Form D
6.
Use pencil and paper to answer the question.
Area of a circle:
Volume of a cylinder:
Answer the following questions.
Use the key on your calculator or use 3.14 as an approximation for
Round your answers to the nearest hundredth.
.
a. What is the area of the base of the cylinder? _______________
b. What is the volume of the cylinder? ________________
ANSWER:
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a. 113.04
b. 904.32
(using 3.14) , or 113.10
(using 3.14) , or 904.78
(using )
(using )
Page 5
Name:
Class:
Date:
Unit 11 PC Form D
7.
Use pencil and paper to answer the question.
The prism shown is made of centimeter cubes.
Volume of rectangular prism:
a.
What is the area of the base of the prism?
b.
What is the height of the prism?
c.
What is the volume of the prism?
d.
If you kept the base the same, but doubled the volume
of this prism, what would the new height be?
________________
(unit)
Write a number sentence to show how you found the
height in part d.
e.
________________
(unit)
________________
(unit)
________________
(unit)
___________________________________________________________
ANSWER:
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a. 4
b. 4 cm
c. 16
d. 8 cm
e.
Page 6
Name:
Class:
Date:
Unit 11 PC Form D
8.
Use pencil and paper to answer the question.
The prism shown is made up of centimeter cubes.
a. What is the surface area of the prism?
________________
(unit)
b. Explain how you found the surface area.
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
______________________________________________________________
ANSWER:
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a. 40
b. Sample explanation:
I found the area of all 3 surfaces that are visible, so I started with the top face.
The area of the top is 8, which is the same as the bottom area. So the top
and bottom area totals 16 (
).
Next I took the area of the right side, 4, and doubled it, since the left side has the same
area. So the right and left side area totals 8 (
).
Then I took the area of the front, 8, and doubled it, to give me the area of the front and
back, which totals 16 (
).
Finally, I added these 3 totals,
to give me the surface area of 40
.
Page 7
Name:
Class:
Date:
Unit 11 PC Form D
9.
Use pencil and paper to answer the question.
What information do you need to figure out how many square feet of paint you would use if you
painted the entire cylinder (top, bottom, sides)?
________________________________________________________________
________________________________________________________________
ANSWER:
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The area of the base, the circumference of the base, and the height.
Page 8
Name:
Class:
Date:
Unit 11 PC Form D
10.
Use pencil and paper to answer the question.
Area of a circle:
Volume of a cylinder:
Volume of a cone:
(
Answer the following question.
Use the key on your calculator or use 3.14 as an approximation for
Round your answer to the nearest hundredth.
.
If you place a cone inside of the cylinder as shown below, and the cone is an exact fit (that is, the
apex of the cone touches the top of the cylinder, and the base of the cone fits exactly at the bottom
of the cylinder), what would the volume of the cone be? Show your work.
________________
(unit)
Write a number sentence to show how you found your answer.
_______________________________________________________________
ANSWER:
209.33
(using 3.14) , or 209.44
Sample work:
(using 3.14)
(using
)
(using
)
=
)
=
=
Sample number sentence:
(using 3.14)
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or (using
)
Page 9
Name:
Class:
Date:
Unit 11 PC Form D
11.
Use pencil and paper to answer the question.
Area of a circle:
Volume of a cylinder:
Answer the following question.
Use the key on your calculator or use 3.14 as an approximation for
Round your answer to the nearest hundredth.
.
If you place a cone inside of the cylinder as shown below, and the cone is an exact fit (that is, the
apex of the cone touches the top of the cylinder, and the base of the cone fits exactly at the bottom
of the cylinder), what would the volume of the cone be? Show your work.
________________
(unit)
Write a number sentence to show how you found your answer.
_______________________________________________________________
ANSWER:
37.68
(using 3.14) , or 37.70
Sample work:
(using
(using 3.14)
(using
)
)
=
)
=
=
Sample number sentence:
(using 3.14)
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or (using
)
Page 10
Name:
Class:
Date:
Unit 11 PC Form D
12.
Use pencil and paper to answer the question.
The pyramid below has a height of 7 in.; the area of its base is
.
What is the volume of the pyramid? Show your work. __________________
(unit)
Write a number sentence to show how you found your answer.
_______________________________________________________________
ANSWER:
(
)
Sample work:
=
Sample number sentence:
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Page 11
Name:
Class:
Date:
Unit 11 PC Form D
13.
Use pencil and paper to answer the question.
Priscilla’s fish are sick, and she wants to add medicine to the tank. The instructions suggest adding
one drop of medicine for every 4 L of water. The base of the fish tank measures 40 cm by 25 cm.
The tank is filled with water to a height of about 20 cm.
1L = 1,000
a. How many drops of medicine should Priscilla add to her tank?
Round your answer to the nearest whole number. ________
b. Explain what you did to find the answer.
______________________________________________________________
______________________________________________________________
ANSWER:
14.
a. 5
b. First I found the volume of the water in the tank by multiplying 40 by 25 by 20.
So the volume was 20,000
, which is 20 L, and
Use pencil and paper to answer the question.
A Treasure Hunt
The intrepid explorer Hope Moore went to the Lost Realm in search of the treasure of the
Vanquished Tribe.
Traps had been set to guard the treasure. Hope fell through the trap door into a 12-foot-high
rectangular room that measured 5 feet wide by 9 feet long.
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Page 12
Name:
Class:
Date:
Unit 11 PC Form D
Suddenly, the room began to fill with water but
stopped when it was 4 feet deep. Hope
sighed with relief, but her relief didn’t last long.
The two 5-foot-wide walls of the room began to
move, making the room smaller and causing the
water level to rise. Every 10 minutes, the walls were
1 foot closer together.
a. Label the rectangular prism with the dimensions of the original room.
b. Figure out how much time will pass before the water lifts Hope to the trap door exit in the ceiling
of the room. Show your work and explain how you found your answer.
ANSWER:
a. Sample answer:
b. The water will reach the top of the room (trapdoor exit) in 60 minutes. I found this by
finding the volume of the original room (
). I then found the volume of
water after the water stopped filling up. (
) From there, I needed to find out
when the volume of the room would match the volume of the water. After every 10
minutes, the length is one foot less, which means that the volume of the room decreases
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Page 13
Name:
Class:
Date:
Unit 11 PC Form D
by 60 cubic feet in that time.
I ended up subtracting 60 a total of 6 times, because
So 10 min.
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.
Page 14