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UNIT 12

Volume and Surface Area

CCM6+

Name: ________________

Math Teacher:___________

Projected Test Date:_____ Main Concept(s) Page(s)

Vocabulary 2

Basics of 3-D Figures 3-7

Surface Area of Prisms and Square Pyramids 8-11

Surface Area of Cylinders 12-13

Surface Area of Compound 3-D Shapes 14-17

Volume of Prisms and Cylinders 18-19

Problem Solving with Volume an Surface Area 20-23

Volume of Rectangular Prisms with Fractional Edges 24-26

Unit Review/Study Guide due ______________ 27-31

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CCM6+ Unit 12 Vocabulary

area the amount of square units covered by a plane figure measured in square units

net an arrangement of two-dimensional figures that can be folded to form a polyhedron (3-D figure)

surface area the sum of the area of the faces of a 3D figure

face a flat surface of a polyhedron (a 3D figure)

edge the line segment along which two faces of a polyhedron intersect

vertices a point where three or more edges intersect

pyramid a polyhedron that has a polygon base and triangular lateral faces

right prism a polyhedron that has two parallel congruent polygon bases. All lateral faces are rectangles.

circle a series of concentric points that are equidistance from a center point

circumference the distance around a circle (like perimeter) it is approximately 3 times the length of the circle's diameter. C=pd

diameter a line segment that begins on a point on the circle's circumference, runs through the center point and ends on another point on the circle's circumference (Twice the radius)

radius a line segment that begins at the circle's center point and ends on a point on the circle's circumference (half the diameter)

volume the number of cubic units needed to fill a given space

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Day 1: 3-D Figures Big Ideas

Warmup:

1. What is the surface area of the cube shown?

Hint: Find the area of each surface.

2. What is the volume of the cube shown?

3. Draw and label all 3-D shapes you can in the space below.

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BASICS of 3-D SHAPES:

Key Words Definition What to look for

Example #1 Example #2

Base

The “bottom” or parallel

polygons on a ________ or the polygon that doesn’t

connect to the apex point on a ____________

Lateral

Having to do with a part of the 3-D shape

that is NOT the _________

All of the lateral parts of a pyramid are what shape?

All of the lateral parts of a prism are what shape?

Prism

2 polygon ______

connected by __________

What shape is the base?

Pyramid

1 polygon ______

connected by ________ to a top _______

This is a ________ pyramid

Face(s)

a flat surface of a _________

or ___________

How many faces? How many edges? How many vertices?

How many faces?

How many edges?

How many vertices?

What is this shape?

Edge(s)

a line segment at the edge of a _________

Vertex

(Vertices)

a corner point of a _________

or a __________

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BIG IDEAS:

Why can’t you just name a shape as a “prism” or a “pyramid?”

What else is required in the name of a 3-D shape?

If a “POLYHEDRON” is only made of polygons, which shapes on this page are NOT polyhedra?

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POLYHEDRON PATTERNS

Complete these charts to discover the polyhedron patterns.

Triangular Prism

Rectangular Prism

Pentagonal Prism

Hexagonal Prism

Base’s # of Sides

# of Faces

# of Vertices

# of Edges

PRISM PATTERNS:

If n=the number of sides on the base shape of the prism, write an algebraic expression for:

the number of faces: ____________________

the number of vertices:___________________

the number of edges: ____________________

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POLYHEDRON PATTERNS Continued

Complete these charts to discover the polyhedron patterns.

Triangular Pyramid

Rectangular Pyramid

Pentagonal Pyramid

Hexagonal Pyramid

Base’s # of Sides

# of Faces

# of Vertices

# of Edges

PYRAMID PATTERNS:

If n=the number of sides on the base shape of the pyramid, write an algebraic expression for:

the number of faces: ____________________

the number of vertices:___________________

the number of edges: ____________________

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DAY 2: Find the SURFACE AREA of rectangular prisms

WARMUP:

Looking at the shape below right, how many faces are there?______

What is the name of this shape?_______________________________

What is the area of each face?

Top:_____________

Bottom:_____________

Left:_______________

Right:______________

Front:_____________

Back:_____________

What do you notice about the areas of the faces?

Can you make a “formula” for the area of a rectangular prism?

*Use dimension names like “length,” “width” and “height.” Variables: l, w, h.

**Make your “l” a cursive loop otherwise it looks like a 1!

***SMILEY FACE METHOD!

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Practice finding SA of rectangular prisms

What is the “FORMULA” for finding SA? SA = ___________________________________

SHAPE L, W, H CALCULATE the SA

l = ________

w = ________

h = ________

SA = _________sq units

l = ________

w = ________

h = ________

SA = _________ cm2

l = ________

w = ________

h = ________

SA = _________ in2

l = ________

w = ________

h = ________

SA = _________ m2

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Day 2: Make or use a NET to find SA by finding the area of each face.

3-D Shape Net of the Shape Area of each face

4x2 = 8 4x3 = 12 4x2 = 8 Surface Area= 3x2 = 6 52 sq units 4x3 = 12 3x2 = 6

Draw in the dimensions on the pyramid

Area of square = ______ Area of triangle = ______ Area of triangle = ______ Area of triangle = ______ Area of triangle = ______ Total Surface Area = _______ cm2

4 in

5 in

3 in

Triangle: ___•___•___=____ Triangle: ___•___•___=____ Rectangle: ___•___=____ Rectangle: ___•___=____ Rectangle: ___•___=____ SA = ______ in2

You draw a net: SA = _________ cm2

You draw a net: SA = ______ in2

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Day 2 HW: USE A CALCULATOR to find the SURFACE AREA…careful…they aren’t all rectangular!

#1

#2

#3

#4

#5

#6

#7

#8

#9

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Day 3: Find SA of cylinders

What is the net of a cylinder?

Draw it:

Practice—Find the SA of the two shapes below.

Cylinder Area of Base Lateral Area Total Surface Area

r = 10 cm h = 20 cm

What is “tricky” when you find the SA of a cylinder?

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Day 3 HW…Use a CALCULATOR! Show your work in the left and bottom margins as needed.

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Day 4: More surface area

Warmup

Cut Nets Stage: 2

The net of a cube has been cut into two. It could be put together in several ways so that it could be folded into a cube.

Here are the nets of 9 solid shapes. Each one of these has been cut into

2 pieces, like the net of the cube.

Can you see which pieces go together?

These are the shapes:

Cube: ___ and ___

Square Pyramid: ___ and ___

Trapezoidal Prism: ___ and ___

Pentagonal Pyramid: ___ and ___

Pentagonal Prism: ___ and ___

Triangular Prism: ___ and ___

Hexagonal Pyramid: ___ and ___

Triangular Pyramid: ___ and ___

Rectangular Prism: ___ and ___

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Day 4: Can we find the SA of combined 3D shapes?

Example 1:

Let’s draw a net of this shape to find the total Surface Area.

Example 2:

You are making a rectangular box to hold your valentines. The box has

dimensions of 8 inches x 10 inches x 5 inches. The box has no top. If you paint the outside of the box, how many square inches will be painted?

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Day 4 HW -- Birdhouse Activity:

Ryan and his father make birdhouses to sell for extra money. All outer surfaces of the birdhouses are painted

bright blue. A half gallon of paint will cover 25 square feet. How many birdhouses could be painted using a

half-gallon of paint?

Questions to consider: Work Space:

1. Paint covers the area in square feet. The birdhouse dimensions are given in inches. How will I represent my dimensions as fractional portions of a foot?

2 inches is ________ft 4 inches is ________ft 6 inches is ________ft 8 inches is ________ ft 10 inches is ________ft 12 inches is ________ft

2. How can I break down the birdhouse into 2-D figures that I know how to calculate the areas of?

3. How do I handle the opening for the birds? That portion will not get painted, so how do I account for that?

8 in

4 in

12 in

10 in

6 in

2 in

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4. I need to draw each section that will be painted and label them with the correct dimensions. Find the AREA of each piece.

For this piece, you need the area of the rectangle that DOES NOT include the circle! 5. TOTAL SURFACE AREA = _____________________ft2 6. Now, how many birdhouses can be painted with a half gallon of paint? *HINT: What will you do with a remainder?

Roof sections: Lower portions:

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Day 5: How can I calculate the VOLUME of prisms and cylinders?

Surface Area is on the ____________________ of a 3-D shape.

Volume is on the _____________________ of a 3-D shape.

Volume is MUCH EASIER than Surface Area because to calculate it you simply

find: Volume = Area of Base Shape • height of 3-D shape

V = Bh

Let’s practice with different 3-D shapes:

Shape Base Shape Dimensions and

Area SHADE the BASE if it

helps

Height of

3-D shape

Calculate the VOLUME

V = Bh

d = 8 mm

h = 12 mm

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Day 5: Homework…Yes, you may use a calculator but show what you typed! There is margin space to help show work!

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Day 6: Practice with V and SA

Warmup:

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Day 6: Practice Problems involving VOLUME to solve with your table:

1. What is the volume of a rectangular prism with a length of 5 m, a width of 6 m, and a height of 12 m?

2. What is the height of a rectangular prism with a length of 10 in., a width of 3 in., and a volume of 210 in.2?

3. What is the volume of a cube with an edge that measures 4 cm?

4. What is the volume of a triangular prism with a height of 6 ft. and a base shape with dimensions 3 ft x 6 ft?

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Day 6 HW

Surface Area and Volume Mixed Word Problems

Directions:

(1) Choose & write whether the problem is asking you to find SURFACE AREA or VOLUME

(2) Write the formula (if needed) which you would use to solve the problem.

(3) Do STEPS 1 & 2 for all problems before you start solving so we can make sure everyone has

the correct formulas to start

(4) Solve

(5) Label your answer with the correct units

1. Elena wants to paint her jewelry box blue. The jewelry box is in the shape of a cube

and has an edge length of 4 in. How much blue paint will Elena need?

2. Nicholas has a pepper shaker in the shape of a cylinder. It has a radius of 9 mm and a

height of 32 mm. How much pepper will fit in the shaker?

3. Reynaldo builds a pool in his backyard. The pool measures 55 feet long, 28 feet wide,

and 9 feet deep. How much water will fit in the pool?

4. How many square feet of cardboard does Jessica need to make a rectangular prism

with length of 16 inches, width of 9 inches, and height of 4 inches?

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5. How much gift wrap is needed to cover a box which measures 3 feet by 2 feet by 3

feet?

6. A package shaped like a cube has an edge that is 28 cm long. How much space is

available to pack inside the box?

7. A cylindrical fish tank is 1 foot tall. The radius of the fish tank is 5 inches. How much

water does it take to fill the tank? (Be careful – look at the units you are given)

8. Kissie needs to paint the top and sides of a rectangular prism. The prism has a length

of 25 mm, a width of 15 mm, and a height of 9 mm. How much paint does she need to

cover the top and sides?

9. Brittany is going to cover the label on a Pringle’s can and decorate it for Easter. The

can has a diameter of 4.5 in. and a height of 14 in. She only needs to cover the label,

not the top or bottom of the can, what is the minimum amount of paper needed?

10. A cereal company decided to make an odd-shaped box for a promotion they are

doing. The new design is a rectangular prism with length of 10 in, width of 8 in., and

height of 4 in. and attached to the rectangular prism is a cylinder with a radius of 2 in.

and a height of 10 in. How much cereal will fit in the box?

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Day 7: What do I do in finding VOLUME if the edges of a rectangular prism are fractions?

A right rectangular prism has edges of 1 ”, 1” and 1 ”. How

many cubes with side lengths of would be needed to fill the

prism? What is the volume of the prism?

Woah…let’s break this down!

Step 1: Remember the birdhouse when we converted inches into feet? Well, here we

need to convert our measures into quarters…so

11

4=

4 1 =

4 1

1

2 =

2=

4

Step 2: If each measure is “fourths” I can draw how many “fourth of a cube” edges

there area on each side.

11

2 =

4

1 = 4

11

4 =

4

Step 3: Using “fourths of cubes,” how many blocks are at each dimension?

Fill these in below:

_____ • _____ • _____ = _____

4 4 4 4

So, how many blocks that are “fourths” are in the volume? _______________

Step 4: Calculate the Volume w/o a calculator:V = ___________ = ___________ = _____ in3

1

4

1

2

1

4

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Day 7: Volume of Prism with Fractional Edge Practice

1. A rectangular container has a length of 6 inches, a width of 2 ½ inches, and height of 4 ¼ inches. What is the Volume?

2. A follower box is 4ft. long, 23

4 ft. wide, and ½ ft. deep. How many cubic feet of

dirt can it hold?

3. Explain why the volume of a cube with side lengths 11

2in, 1

1

2in , 1

1

2in is 9

1

8 𝑖𝑛3.

Draw the diagram to match this prism.

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Day 7 HW: Volume Fractional Edge Length Word Problems

1. A right rectangular prism has edges of, 21

4 in, 2 in and 1

1

2in. How many cubes with lengths of

1

4in

would be needed to fill the prism? What is the volume?

2. Find the volume of a rectangular prism with dimensions 11

2 in , 1

1

2 in and 2

1

2 in .How many cubes

with lengths of 1

2 in would be needed to fill the prism?

3. A follower box is 3feet long, 1 3

4 feet wide, and

1

2 feet deep. How many cubic feet of dirt can it

hold?

4. Draw a diagram to match the rectangular prism whose length is 51

2in, width is 4in and height is

41

2in.

5. Use centimeter grid papers to build a rectangular prism with the volume of 24 cubic units. At least

one of the side lengths of the prism is a fractional unit. What are the dimensions of the rectangular

prisms you built? What is the surface area of the prism?

6. Mr. White is trying to store boxes in a storage room with length of 8yd, width of 5yd and height of

2yd. How many boxes can fit in this space if each is box is 21

4 feet long 1

1

2 feet wide and 1 foot

deep ?

7. Linda keeps her jewelry in a box with dimensions 81

4 in by 3

3

4 in by 4in. Find the volume of

Linda’s jewelry box.

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