lesson 16: surface area and volume

8/8/2019 Lesson 16: Surface Area and Volume

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LESSON 16: SA and Volume December 10, 20

DO NOW!Which two rectangles have the same area but different perimeters?


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LESSON 16:

What are Surface Area and Volume?

Standards: 7.G.2, 7.G.3, and 7.G.4


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Three-Dimensional Shapes

CylinderCone

Cube

Sphere

What are the faces of these shapes?


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COMPLETE THE QUIZ!


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What is Surface Area?Surface area is the sum of the area of the faces of a prism.

What is the surface area of this rectangular prism?

Length = 4 unitsWidth = 3 unitsHeight = 5 units

Using nets to find the surface area...

So... What would the net of the above prism look like?


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lw

Top

lh

Side 1

lw

Base

lh

Side 2

hw

Back

hw

Front

Surface

Area

Height

Length

Height

CREATE YOUR OWN NET FOR A RECTANGULAR PRISM!

Width

Width Width

WidthWidth

Width

Follow these steps:

Firstly, choose a length,width, and height.Example:

L = 6 W = 1 H = 3

Secondly, draw!

Thirdly, cut out and makesure it folds to create aprism.

Finally, find the area foreach side and then the totalsurface area!

Top

BASESIDE 1 SIDE 2

FRONT

BACK

3

6

311 1

1 11

Top

BASESIDE 1 SIDE 2

FRONT

BACK

6


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First, think of the prism's net...

4

33

33

1

1

Use the formula!

Length = 4Width = 3Height = 1


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A Formula for the Surface Area of Rectangular Prisms

Surface Area = lh + lw + lh + lw + wh + wh= 2 (lh + lw + wh)


We can just input the values!


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DO NOW: What is the surface area of this cube?

Like a regular rectangular prism, you can start by thinking about the net.

So... What is the surface area of a cube?

6s2


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L =W =H =

3 cm

2 cm

2 cm

1 cm

2 cm

2 cm

1 cm

Using the formula, find the surface area of this prism.

OR L =W =H =

OR L =

W =H =


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Surface Area of a Rectangular Prism = 2(lw + lh + wh)

Find the surface area!

l =w =h =


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Calculate the surface area of each prism.


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Complete the LEARNING LOG - 7.G.4!

EXTRA CREDIT(5 points on top of your test score this week!)The surface area of a rectangular prism is 48 square feet. The areaof its front is 4 square feet, and the area of one side is 10 square feet.

What is the area of the top of the prism?


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What is Volume?

Volume refers to the amount of space an objecttakes up. To figure out the volume of a box, youneed three measurements.

You need to know the length, the width, and theheight of the box, to figure out its volume.

length

width

height

To calculate the volume of a box, you multiply itslength by its width by its height. This is shown by

the formula lx wx h.

How many units long is the box?

How many units wide is the box?

How many units high is the box?

How can we use this to figure out the volume?

Volume of the box =

Does it matter in which order we multiply thesevalues?

NO! Which property says so?

Volume units are always measured in which kind ofunits?

How many dimensions does a cube have?!


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Find the volume of each of the following rectangular prisms!


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2 ft

4 ft1 ft

80 ft

30 ft

60 ft

30 cm

20 cm10 cm

Find the volume of each of the following!


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l =

w =

h =

cm

cm

cm?

?

?

Design a box that has a volume of 18 cm3


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l = 3

w = 4

h =3

4

4

?

in

in

in

This box has a volume of 48 in3

. What is the height of the box?


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30 in? in

The volume of the empty tank is 7,200 in3

LEARNING LOG - 7.G.2 - Fish Tank!

Find the height and the width of the fish tank. Is your choice

the only possibility? Explain and show your work!

? in


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USING FORMULAS!

As long as you are given the formula, you only have to input the values.

12 cm

5 cm

3 cm

4 cm

5 cm

What are the surface area andvolume of this right triangular prism?


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Surface Area

Find the surface area of the cylinder.Round to the nearest tenth. 2 cm

3 cm

Can you create a net for this?

CYLINDERS!

Lateral Area

So what is the formula for the surface area of a cylinder?

S.A. of a Cylinder = 2r2

+ hd


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1. A cylindrical oatmeal can has a 6 inch diameter and aheight of 8 inches. What is its surface area?

2. What is the lateral area of the following cylinder?

3. What is the surface area of the entire cylinder?

PROBLEMS

h = 10 in

r = 5 in


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Volume of Cylinders

.3 in12 in

.6 in14 in 13.5 in

.3 in

The formula for finding the volume of a cylinder is

volume =x r x h2

Find the volume of the following cylinders. Remember to express theanswer in cubic measurement. Use 3.14 as the value for .


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40 ft

6ft

How much does this tanker hold?

lesson 16: surface area and volume

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