How much cardboard does it take to make a cereal box?

Have you ever

wondered?

Surface Area- the sum of the areas of all the faces

Do you see the RED

face?

4 in.

7 in.

10 in.

What are the dimensions of this rectangle?10 in.

4 in.

Do you see another face that is just like the RED face?

Where is it located?

4 in.

7 in.

10 in.

Yes, it’s on the back.

10 in.

4 in.

10 in.

4 in.

Now there are 2 rectangles

40 in2

40 in2 that each have an

area of 40 sq. in.

4 in.

7 in.

10 in.

Do you see the BLUE face?

What are the dimensions of this rectangle?

4 in.

7 in.

Do you see another face that is just like the BLUE face?

Where is it located?

4 in.

7 in.

10 in.

Yes, it’s on the left side.

4 in.

7 in.7 in.

4 in.

Now there are 2 rectanglesthat each have an area of 28 sq. in.

28 in2

28 in2

4 in.

7 in.

10 in.

Do you see the GREEN face?

What are the dimensions of this rectangle?

10 in.

7 in.

Do you see another face that is just like the GREEN face?

Where is it located?

4 in.

7 in.

10 in.

Yes, it’s on the bottom.

10 in.

7 in.

10 in.

7 in.

Now there are 2 rectanglesthat each have an area of 70 sq. in.

70 in2

70 in2

Now we just need to add all the areas of the sides together.

+ +

++ 70 in2

28 in2

40 in2

40 in2

28 in2

70 in2

The total Surface Area for this rectangular prism is

40 + 40 + 28 + 28 + 70 + 70 =

276 in2

It’s your turn to try

one!

Find the surface area.

6 cm

3 cm2 cm

Area of top and bottom:

3 cm x 2 cm = 6 cm22

Since there are two of these shapes,

6 cm2 x 2 = 12 cm12 cm22

Find the surface area.

6 cm

3 cm2 cm

Area of front and back:

3 cm x 6 cm = 18 cm2

Since there are two of these shapes,

18 cm2 x 2 = 36 cm36 cm22

Find the surface area.

6 cm

3 cm2 cm

Area of both sides:

6 cm x 2 cm = 12 cm2

Since there are two of these shapes,

12 cm2 x 2 = 24 cm24 cm2

Find the surface area.

6 cm

3 cm2 cm

Now add up the answers

12 cm12 cm22

36 cm36 cm22

+24 cm+24 cm22

72 cm72 cm22

Formula for Surface Area of Rectangular Prisms

SA = 2(lw) + 2(lh) + 2(wh)

width

height

length

Formula for Surface Area of a Cube

SA = 6(s2)

side

side

sideSince all dimensions of a cube are the same, you only need to know the length of one side.

End

of

day 1

How much metal is used to make a soup can?

Surface Area of a cylinder = Area of top + Area of bottom + Area of the side

TOP

BOTTOM

SIDE

Area of a circle is πr2.

Since there are 2 circles that make up the

net of a cylinder then,

the area is 2(πr2).

The area of a rectangle is the product of the two sides. One side is the height of the can, the other side is the circumference of the circle, since the label wraps once around the can.

h

C=2πr

So the area of So the area of the rectangle the rectangle

is (2is (2ππr)h.r)h.

C

Add those two parts together and you have the formula for the surface area of a cylinder.

Surface Area of a Cylinder =

2(π r 2) + (2 π r)hCircles + Rectangle

Example 1:Example 1:

Find the surface area of this cylinder.

r = 3 cm

h = 6 cm