Name _______________________________________
Date ___________________________
COURSE: MSC V
MODULE 2: Fundamentals of Geometry
UNIT 3: Volume & Surface Area
As you work through the tutorial, complete the following questions.
1. What do you measure using cubic feet—perimeter, area, distance,
volume, or weight? ______________________________________________
2. __________ is a three-dimensional measurement that describes how
much __________ an object takes up.
3. Dijit is trying to find the volume of what? ____________________________
4. If B is the area of the base rectangle of the prism, then b 3 h 3 l can be
written as ______________________________________________________ .
5. What does B represent? __________________________________________
What does b represent? __________________________________________
6. A prism that is formed by a series of rectangles is called a(n) __________
Key Words:
Volume
Triangular prism
Rectangular prism
Right prism
Length
Width
Height
Base
Learning
Objectives:
• Classifying a
prism according
to its base
• Identifying right
prisms
• Expressing the
volume of a right
triangular prism
V 5 1}2} (bh)l
• Calculating the
volume of a right
triangular prism
________________________________________________________________.
7. A prism in which all the faces are rectangles and all the sides that meet
are perpendicular to each other is called a(n) ______________________ .
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8. What kind of prism is Dijit’s new apartment? ________________________
9. What is the formula for the volume of a right triangular prism in terms of
b, h, and l ?
__________________________________________________ .
10. What is the volume of Dijit’s new apartment? ________________________
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Name _______________________________________
Date ___________________________
COURSE: MSC V
MODULE 2: Fundamentals of Geometry
UNIT 3: Volume & Surface Area
Dijit decides to build a glass table to go with his couch. Sophie designs the
table below. It is a hollow prism that she will fill with brightly colored marbles.
24 in.
50 in.
20 in.
16 in.
1. What kind of prism is the table?
__________________________________
2. Sophie needs to calculate the quantity of marbles she will need to fill the
table. Should she find the area, the surface area, or the volume?
________________________________________________________________
Explain your answer.
____________________________________________
________________________________________________________________
3. What formula can Sophie use to calculate the quantity of marbles she
will need? ______________________________________________________
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4. What formula can Sophie use to find the area of the triangular base, B,
in terms of b and h? ______________________________________________
5. Using the measurements in the figure above, find the area of the base.
Include the correct unit in your answer. ______________________________
6. Find the volume of the table. Include the correct unit in your answer.
________________________________________________________________
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Name _______________________________________
Date ___________________________
COURSE: MSC V
MODULE 2: Fundamentals of Geometry
UNIT 3: Volume & Surface Area
As you work through the tutorial, complete the following questions.
1. What does Dijit need to calculate before Sophie can buy the aluminum
foil for the walls of his new apartment?
____________________________
2. The __________ __________ of a prism can be found by finding the sum
of the areas of the __________ of the prism.
3. Why doesn’t Dijit need to find the entire surface area of his apartment?
Key Words:
Surface area
Triangular prism
Right prism
Faces
Base
Height
Triangle
Rectangle
Learning
Objectives:
________________________________________________________________
• Defining the
surface area of
an object
4. How does Dijit find the area of each rectangular wall? ________________
• Defining the
faces of a right
triangular prism
________________________________________________________________
5. How does Dijit find the area of each triangular wall? __________________
________________________________________________________________
• Recognizing a
foldout for a right
triangular prism
• Calculating part
of the surface
area of a right
triangular prism
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6. The __________ of a prism are the flat surfaces that make up the prism.
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Name _______________________________________
Date ___________________________
COURSE: MSC V
MODULE 2: Fundamentals of Geometry
UNIT 3: Volume & Surface Area
Dijit is afraid that the glass table will get scratched. Sophie tells him that he
can cover the outside glass with a thin, transparent, scratch-resistant film.
24 in.
50 in.
20 in.
16 in.
1. Sophie needs to calculate how much film she will need to cover the
table. Is this quantity surface area or volume? ________________________
Explain. ________________________________________________________
2. How many surfaces does the table have?
3. Which surfaces have the same area?
__________________________
______________________________
4. What are the dimensions of the top face of the table?
________________________________________________________________
5. What is the area of the top of the table? ____________________________
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6. What are the dimensions of each of the two rectangular sides? ________
7. What is the area of each rectangular side? __________________________
8. What are the dimensions of each triangular end of the table?
________________________________________________________________
9. What is the area of each triangular end?
__________________________
10. What is the total surface area of the table? __________________________
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MATH
Name _______________________________________
Date ___________________________
COURSE: MSC V
MODULE 2: Fundamentals of Geometry
UNIT 3: Volume & Surface Area
As you work through the tutorial, complete the following questions.
1. In a right cylinder, the length of the cylinder is ________________________
to the bases.
2. What is the formula for the area of a circle? ________________________
3. How do you find the volume of a cylinder? __________________________
4. What is the relationship between radius and diameter of a circle? ______
________________________________________________________________
5. The ____________________ of a circle measures the perimeter of a circle.
6. What is the formula for circumference?
____________________________
Key Words:
Volume
Right cylinder
Surface area
Perimeter
Circumference
Pi (p)
Diameter
Radius
Length
Learning
Objectives:
• Calculating the
volume of a right
cylinder
• Calculating the
circumference
of a circle
• Calculating the
surface area of
a right cylinder
7. How does the circumference of the circles relate to the rectangular face?
________________________________________________________________
________________________________________________________________
8. What is an approximation for p, rounded to the nearest hundredth?
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________________________________________________________________
9. What does r represent in the formula for the circumference of a circle
and in the formula for the area of a circle? __________________________
________________________________________________________________
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Name _______________________________________
Date ___________________________
COURSE: MSC V
MODULE 2: Fundamentals of Geometry
UNIT 3: Volume & Surface Area
Sophie will need enough marbles to fill a volume of 9,600 cubic inches for
Dijit’s table. She asks Dijit to buy the marbles. Dijit visits a craft store and
studies a tub full of marbles. He needs to calculate the volume of marbles in
this tub.
18 in
MARBLES
18 in
He measures the tub and sketches the figure below.
1. The bottom of the tub is a circle. Dijit remembers that he needs to
calculate the area of the bottom of the tub in order to find the volume.
The volume of the tub is the __________ of the base times the __________
of the cylinder.
2. What is the value of r for this tub?
________________________________
3. Using 3.14 as an approximation for p, what is the area of the circular
base? Round your answer to the nearest tenth, and use the correct unit
____________________________________________________
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of measure.
________________________________________________________________
4. What is the volume of marbles in the tub? Round your answer to the
nearest tenth, and use the correct unit of measure. ____________________
5. If Dijit buys the entire tub, will there be enough marbles to fill his table?
_____________________
If not, what quantity of marbles are still needed? ____________________
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Name _______________________________________
Date ___________________________
COURSE: MSC V
MODULE 2: Fundamentals of Geometry
UNIT 3: Volume & Surface Area
Calculating the Volume of a Right Triangular Prism
1. In the figure below, b = 5 inches, h = 5 inches, and l = 20 inches.
h
l
b
a. Identify the type of prism. ______________________________________
b. What is the value of the area of the base, B? ______________________
c. What is the volume of the prism? ________________________________
Calculating the Surface Area of a Right Triangular Prism
2. Follow the steps below to find the surface area of the prism above. Show
your work. Include the correct units of measure in your answers.
a. How many faces does the prism have?
__________________________
b. What is the area of each square base of the prism? ________________
______________________________________________________________
c. What is the area of each rectangular surface of the prism? __________
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______________________________________________________________
d. What is the total surface area of the prism?
______________________
Calculating the Volume & Surface Area of a Right Cylinder
3. A right cylinder has a radius of 10 inches and a length of 24 inches. Use
3.14 to approximate p.
a. Find the area of the base of the cylinder.
________________________
b. Find the volume of the cylinder. __________________________________
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Name _______________________________________
Date ___________________________
Putting It All Together
4. A high school drama department will stage Shakespeare’s Julius Caesar.
To make some columns for an ancient Roman building, the drama teacher
bought huge foam cylinders. To buy paint for the cylinders, the students
need to find the total area of a column. The teacher knows that each
cylinder is 18 ft long and has a volume of 226 ft 3.
a. Without performing the calculation, explain how to find the area of
each circular base of the column. ________________________________
______________________________________________________________
b. Find the area of each circular base. Round your answer to the nearest
tenth. ________________________________________________________
c. Without performing the calculation, explain how to find the radius of
each circular base. ____________________________________________
______________________________________________________________
d. Find the radius. Round your answer to the nearest whole number.
______________________________________________________________
e. You know the area of the two bases of the column. What else must
you find in order to calculate the whole surface area? ______________
______________________________________________________________
f. Find the surface area of the column. Round your answer to the nearest
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whole number. ________________________________________________
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MATH
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Name _______________________________________
Date ___________________________
COURSE: MSC V
MODULE 2: Fundamentals of Geometry
UNIT 3: Volume & Surface Area
1. How are a right triangular prism and a right rectangular prism different
from each other? ________________________________________________
________________________________________________________________
2. What formula do you use to find the area of a circle? ________________
3. If you know the area of the base of a right cylinder and the length of the
cylinder, how do you find the volume? ______________________________
4. How are diameter and radius related? ______________________________
________________________________________________________________
5. How are circumference and radius related?
________________________
________________________________________________________________
6. How many rectangular faces does a right triangular prism have?
________________________________________________________________
7. To calculate the volume of a right rectangular prism, a friend multiplies
b × l. Is this correct? If not, what was done wrong? __________________
________________________________________________________________
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________________________________________________________________
8. In a right cylinder, what shape is the base? __________________________
________________________________________________________________
9. What dimensions do you need to know to find the surface area of a right
triangular prism? ________________________________________________
________________________________________________________________
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Name _______________________________________
Date ___________________________
10. In the space below, draw a net or pattern, for an unfolded right
triangular prism.
11. Pictured below are a right rectangular prism and a right triangular prism.
How tall should the triangular prism be so that it has the same volume as
the rectangular prism? Show your work.
3 in.
4 in.
3 in.
4 in.
8 in.
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