4.1 creating objects from nets · a paper box measures 4.5 cm x 5.0 cm x 3.0 cm. what is the volume...

4.1

Exploring Nets

4.2

Creating Objects from

Nets

You and your partner will receive one 3D shape.

1)Name each face of the object2)Trace each face3)Connect the faces that you drew

INVESTIGATE

Net

PolyhedronNet

Polyhedron

edgevertextwo faces meet _____

three or more edges meet

at a ________vertex

Name that shape

Example 1. What shape will this net make?

Example 2. What shape will this net make?

Example 3. What shape will this net make?

Example 4. What shape will this net make?

icosahedron

Example 5. What shape will this net make?

Example 6.

What does it mean by “right”?

Draw the following net of this

rectangular prism!

Example 7.

Predict what shape this will make?

**We name our shapes depending on our base shape

Example 8.

Example 9.

Example 10.

Review 1.

With the person next to you, create a Rectangular prism from 10 or less blocks.

1. Determine the surface area in as many different ways as you can think of.RECORD each way.

2. Can you come up with a definition of surface area?

What is area?...

What about surface area?

INVESTIGATE

How do we find area of square OR rectangle?

Surface Area: Is the addition of ALL AREAS of the panels on our

3D shape!

Calculate the total surface area!

Reminder!

Tip of the day:

BE ORGANIZED!!!

Example 1.

Calculate the total surface area!

*Look for similar faces

Example 2.

Example 3.

Calculate the total surface area!

Example 4.

Find the surface area of this cube

3cm

**Use what we know about cubes to make your life easier

Section 4.4

Surface Area of a Right Triangular Prism

With your partner…

1) Determine the area of the rectangle shown

2) Using the full sides of the rectangle, create a triangle.

3) What would the area of this triangle be?

4) Create your own formula for finding the area of a

triangle

What is half the

area?

INVESTIGATE

Area of a triangle =

**Pay close attention to which height we are using

Example 1.

Calculate the total surface area

5

Reminder**Be Organized!

Example 3.

Example 4.

Calculate the surface area

shut so students can't get out

What does the net of a cylinder look like?

With your partner….1) You will receive the shapes that you need to make a cylinder2) Cut these shapes out and make a cylinder3) Using what you already know about circles and area, see if you can find the surface area of your shape.

INVESTIGATE

Hint***What is the distance around the circle? How could this help us

Area?

Area?

Radius

How would we find surface area?

Radius

Area?

2πr πd

How does this relate to length of the curved

surface?

The distance all the way around the circle is called the

circumference...this is the same as the width of our curved

lateral surface!

Those lines are the same distance!

Circumference = radius

We use this to find the area of our curved

lateral surface....

h A = l x w

So therefore our surface area of a cylinder is found by finding the area of:Our ___________ circlesOur _______________________ curved lateral surface

Example 1. With your partner, calculate the surface area

Example 2.Calculate Surface Area

Example 3.

We are wrapping presents and we want to use the least

amount of wrapping paper possible. Should we choose...

a) Box with dimensions of 8cm by 3cm by 7cm

b) Cylinder Tube with a radius of 3cm and a height of 6 cm

4.1 - 4.4 & 4.7

NETS AND SURFACE

AREA

Draw and label the net of this triangular prism

Name these 4 nets....

What are the area of these shapes?

3 cm

6 cm

4 cm

5 cm

Calculate the total surface area of the 3-D Object

We want to design a bike ramp that has the following dimensions. How

much area of wood do we need to do so? The ramp does not need a

base.

Find the surface area of the cylinder

We must repaint an entire swimming pool.

The pool is 4m long, 2m wide, and 3m deep.

How much area do we have to cover?!?

**Hint: Is there a top?

What is the Surface Area of this triangular prism?

What is the area of this circle?

We are making aluminum flower pots shaped like cylinders.

There is a bottom on each pot, but no top.

If the pots are 9 inches in height and have a diameter of 12 inches, how many square inches

of aluminum are needed for each pot?

Now we want to paint this flower pot. However, we don't need to paint the bottom...How

much surface area do we have to cover?

What is this part of the

cylinder called?

Find the Surface Area of this net....

What is the difference

between Surface Area and

Volume???

Create the following rectangular prism with linking cubes.1) 2 x 4 x 32) How do we find the volume of this object?3) Is there more than one way to do this?

INVESTIGATE

Finding the volume of a rectangular prism

- How much can we fill this up?

So what is the volume?!?

We have 4 layers of (3x6)

Volume = l x w x h

General Formula for 3D Shapes

V = (area of base)x(height)

Example 1.

We are filling paper boxes with toys and supplies for children that are

homeless. A paper box measures 4.5 cm x 5.0 cm x 3.0 cm. What is

the volume of the box?

What about this triangular prism?

Reminder**General FormulaV = (area of base)x(height)

Volume of a Triangular Prism

V = area of base shape x height

V = bh x h

2

Don’t get confused!This is the height of the entire prism (NOT the triangle)

Example 2.

You're going camping and you want to know how much room you have

in your tent. What is the volume of a tent with these dimensions?

Example 3.

Find the Volume.....

Hint* They did half of the work for you!

Example 4.

Challenge Question

Can you and your partner find the volume of this milk carton?

4.8

Volume of a Right Cylinder

What is the volume?Review!

Triangular Prism

V = base area x height

V = bh x H2

Using our general formula for volume, how do you think we find

the volume of a cylinder?

Volume of a Cylinder

V = area of base x height

V = x h

Example 1.

A hockey puck is a solid piece of rubber with the dimensions shown.

How much rubber is used to make a hockey puck?

Which of these cylinders will hold more? Or are they

the same?

Calculate the volume to find out

The radius has a greater effect!

r2

Hint* Pay close attention to our measurements

Example 2.

What is the volume of this greenhouse?

Example 3.

Challenge Question!

Quiz Review!!!!!

1. Read the Question

2. Discuss and solve quietly with your group

3. Reveal your answers

4. Get points

Find the volume of this rectangular prism.

Calculate the volume

Find the volume

How much does this fish tank hold?

What is the volume of this 3-D object?

Volume?

Find the volume!

The area of the base of a right triangular prism is

14.5 cm² and the length of the prism is 6 cm.

Calculate the volume of the prism.

What is the Volume?

Tally up your points!!

Good Luck :)

Which of the following are nets?

What 3-D objects will those nets make?

This is an incomplete net for a triangular prism. What

shapes must you add to complete this net?

What shape will this net make?

What is the surface area of this net?

What is the Surface Area of this box?

What about the volume?

Find the Surface Area

What is the surface area of this closed cylinder?

The Surface Area of a cube is 216 cm².

How long is one of the edges of the cube?

What is the surface area of the house? (It’s a house, so we

don’t need the bottom!)

Which can of cat food is the better deal?!

What is the volume of a triangular prism with the following

dimensions?

A paper cup has the shape of a perfect cylinder that is 6.9 cm

tall and 3 cm across.

What is the surface area of the cup?

What is the volume?!

What is the name of this prism!?

What is the volume?!