Please start Bellwork # HW, red pen, book on desk.

Please start Bellwork #

HW, red pen, book on desk.

3-23-11

HW, red pen, book on desk.

Surface Area: Prisms and Cylinders

Lesson 10-5 p.527

Surface Area

Surface area is the area of the sum of all of the surfaces of a space figure.

In other words, it is the area of the net.

Surface Area

3 cm

3 cm

2 cm5 cm

Notice that there are 2 bases (front and back) that are identical. There are also two faces (the top and bottom) that are identical.In addition there are two sides (right and left) that are identical.

Surface Area

To find the surface area, find the area of each surface and add them together.

3 cm

3 cm

2 cm5 cm

First, let’s calculate the front and back:A = bhA = 3 (2) = 6 sq. cm. for the front and 6 sq. cm. for the back.

Next, let’s look at the top and bottom:A = bhA = 5 (3) = 15 sq. cm for the top and 15 sq. cm for the bottom.

Last, let’s calculate the right and left sidesA = bhA = 5 (2) = 10 sq. cm for the right sideand 10 sq. cm for the left side.

Surface Area

To find the surface area, find the area of each surface and add them together.

3 cm

3 cm

2 cm5 cm

First, let’s calculate the front and back:A = bhA = 3 (2) = 6 sq. cm. for the front and 6 sq. cm. for the back.

Next, let’s look at the top and bottom:A = bhA = 5 (3) = 15 sq. cm for the top and 15 sq. cm for the bottom.

Last, let’s calculate the right and left sidesA = bhA = 5 (2) = 10 sq. cm for the right sideand 10 sq. cm for the left side.

If we add up all the areas,(6 + 6 + 15 + 15 + 10 + 10)we get 62 sq. cm. That is thetotal surface area of the prism.

Surface Area

Another way to calculate the surface area is to measure the net:

3 cm

3 cm

2 cm5 cm

3 cm

2 cm

5 cm

Surface Area

Another way to calculate the surface area is to measure the net:

3 cm

3 cm

2 cm5 cm

3 cm

2 cm

5 cm

If you calculate the area of each face (or piece)the answer is still 62 sq. cm.

10 15 10

15

6

6

Try This

Find the surface area:

10 in

4 in

3 in

Try This

Find the surface area:

10 in

4 in

3 in

164 sq. in.

Surface Area

We can do the same procedure with a triangular prism:

3 ft

4 ft

6 ft5 ft

How many faces or surfaces are there?

Surface Area

We can do the same procedure with a triangular prism:

3 ft

4 ft

6 ft5 ft

How many faces or surfaces are there?Notice there are 5 surfaces.There are 2 triangles, there is the back,the floor or bottom, and the slanted face.

Surface Area

First calculate the triangles: A = bh 3 (4) = 6 sq. ft. (1st triangle)

2 2 6 sq. ft. (2nd triangle)

3 ft

4 ft

6 ft5 ft

Surface Area



Next calculate the back: A = bh A = 6 (3) = 18 sq. ft. (back)

Next is the floor: A = bh A = 6 (4) = 24 sq. ft. (floor)

3 ft

4 ft

6 ft5 ft

Surface Area





Add them all up for a total of 84 sq. ft.

3 ft

4 ft

6 ft5 ft

Surface Area





Finally find the area of the slant:

A = bh = 6 (5) = 30 sq. ft.

Add them all up for a total of 84 sq. ft.

3 ft

4 ft

6 ft5 ft

Surface Area

We can also calculate the area of a cylinder.

3 m

5 m

What are the shapes that make up acylinder?

Surface Area

We can also calculate the area of a cylinder.

3 m

5 m

What are the shapes that make up acylinder?Did you remember that there are two circles, and a rectangle?

Surface Area

This one is best calculated by looking at the net.

3 m

It is easy to calculate the area of the circles,

2r = 3.14 (3)2

= 28.26 sq. m

(remember there are 2circles so multiply 28.26times 2 to get 56.52 sq. m

5 cm

Surface Area

So we know the circles have a total of 56.52 sq. m. but what about the rectangle?

3 m

5 cm

We can easily see that the heightIs 5 cm, but what is the value ofthe base?

Surface Area

So we know the circles have a total of 56.52 sq. m. but what about the rectangle?

3 m

5 cm

We can easily see that the heightIs 5 cm, but what is the value ofthe base?

The base of the rectangle is theCIRCUMFERENCE of the circle.

Surface Area

3 m

5 cm

To find the circumference of the circle, remember the formula is d

So, C = 3.14 (6) = 18.84 cm

Surface Area

3 m

5 cm

To find the circumference of the circle, remember the formula is d

So, C = 3.14 (6) = 18.84 cm

18.84 cm

OK, so A = bh A = 18.84 (5)

= 94.2 sq. cm.

Remember that the area of theTwo circles totaled 56.52 sq. cm?

The last step is to add the 94.2 Plus the 56.52 to get a total of150.72

Try This

Find the surface area

10 ft

4 ft.

Try This


10 ft

4 ft.

First find the area of the two circles. What is the total of The two circles?

Try This


10 ft

4 ft.

First find the area of the two circles. What is the total of The two circles?

100.48 sq. ft.

Try This


10 ft

4 ft.100.48 sq. ft. (area of the two circles)

Next find the area of the rectangle. The base is the sameas the circumference of the circle. Find the circumferenceof the circle.

25.12 cm

Try This


10 ft


25.12 cm = the base of the rectangle.

Find the area of the rectangle:

Try This


10 ft


25.12 cm = the base of the rectangle.

Find the area of the rectangle:

A of rectangle = 251.2 sq ft.

Try This


10 ft



Now find the total surface area.

Try This


10 ft



Now find the total surface area.

351.68 sq. ft.

PA#42

P.530 #1-6

Print out CAT 6 Review for 7th grade standards.

3-23-11

PA#43

P.530 #8-13

Print out CAT 6 Review for 7th grade standards. Pages 9-30

Please start Bellwork # HW, red pen, book on desk.

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