Surface Areas of Prisms, Cylinders, and Spheres
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Surface Areas of Prisms, Cylinders, and Spheres. 9-4. Course 2. Warm Up. Problem of the Day. Lesson Presentation. Surface Area of Prisms, Cylinders, and Spheres. 9-4. Course 2. Warm Up Find the volume of each figure to the nearest tenth. Use 3.14 for  .

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9 4

Surface Areas of Prisms, Cylinders, and Spheres

9-4

Course 2

Warm Up

Problem of the Day

Lesson Presentation


9 4

Surface Area of Prisms, Cylinders, and Spheres

9-4

Course 2

Warm Up

Find the volume of each figure to the nearest tenth. Use 3.14 for .

1.rectangular pyramid 7 ft by 8 ft by 10 ft tall

186.7 ft3

2. cone with radius 2 ft and height 3 ft

12.6 ft3

33.5 ft3

3. sphere with diameter 4 ft

4. triangular pyramid with base 54 ft2 and

height 9 ft

162 ft3


9 4

Surface Area of Prisms, Cylinders, and Spheres

9-4

Course 2

Problem of the Day

When my age is divided by 2, 3, 4, or 6 there is always a remainder of 1, but when it is divided by 7 there is no remainder. How old am I?

49


9 4

Surface Area of Prisms, Cylinders, and Spheres

9-4

Course 2

Learn to find the surface area of prisms, cylinders, and spheres.


9 4

Surface Area of Prisms, Cylinders, and Spheres

9-4

Course 2

Insert Lesson Title Here

Vocabulary

net

surface area


9 4

Surface Area of Prisms, Cylinders, and Spheres

9-4

Course 2

If you remove the surface from a three-dimensional figure and lay it out flat, the pattern you make is called a net. You can construct nets to cover almost any geometric solid.


9 4

Surface Area of Prisms, Cylinders, and Spheres

9-4

Course 2

Since nets allow you to see all the surfaces of a solid at one time, you can use them to help you find the surface area of a three-dimensional figure. Surface area is the sum of the areas of all surfaces of a figure.


9 4

Surface Area of Prisms, Cylinders, and Spheres

9-4

S = lw +lh + wh + lw + lh + wh

= 2lw + 2lh + 2wh

w

h

l

Course 2

You can use nets to write formulas for the surface area of prisms. The surface area S is the sum of the areas of the faces of the prism. For the rectangular prism shown,

Top

Left

Right

Back

Front

Bottom


9 4

Surface Area of Prisms, Cylinders, and Spheres

9-4

Course 2

Additional Example 1: Finding the Surface Area of a Prism

Find the surface area of the prism formed by the net.

S

= 2lw + 2lh + 2wh

S

= (2 · 15 · 9)+ (2·15 · 7)+ (2 · 9 · 7)

Substitute.

S = 270 + 210 + 126

Multiply.

S = 606

Add.

The surface area of the prism is 606 in2.


9 4

Surface Area of Prisms, Cylinders, and Spheres

9-4

Course 2

Try This: Example 1

4 in.

Find the surface area of the prism formed by the net.

6 in.

3 in.

3 in.

4 in.

S

= 2lw + 2lh + 2wh

S

= (2 · 4 · 6)+ (2·4 · 3)+ (2 · 6 · 3)

Substitute.

S = 48 + 24 + 36

Multiply.

S = 108

Add.

The surface area of the prism is 108 in2.


9 4

Surface Area of Prisms, Cylinders, and Spheres

9-4

Circumference

of cylinder (2r)

r

h

Course 2

If you could remove the lateral surface from a cylinder, like peeling a label from a can, you would see that it has the shape of a rectangle when flattened out.

You can draw a net for a cylinder by drawing the circular bases (like the ends of a can) and the rectangular lateral surface as shown below. The length of the rectangle is the circumference, 2r, of the cylinder. So the area of the lateral surface is 2r. The area of each base is r2.



9 4

Surface Area of Prisms, Cylinders, and Spheres

9-4

Course 2

Additional Example 2: Finding the Surface Area of a Cylinder

Find the surface area of the cylinder formed by the net to the nearest tenth. Use 3.14 for .

6 ft

8.3 ft

6 ft

S = 2r2 + 2rh

Use the formula.

S  (2 · 3.14 · 62) + (2 · 3.14 · 6 · 8.3)

Substitute.

S  226.08 + 312.744

Multiply.

Add.

S 538.824

Round.

S 538.8

The surface area of the cylinder is about 538.8 ft2.


9 4

Surface Area of Prisms, Cylinders, and Spheres

9-4

Course 2

Try This: Example 2

Find the surface area of the cylinder formed by the net to the nearest tenth. Use 3.14 for .

9 ft

20 ft

9 ft

S = 2r2 + 2rh

Use the formula.

S  (2 · 3.14 · 92) + (2 · 3.14 · 9 · 20)

Substitute.

S  508.68 + 1130.4

Multiply.

Add.

S 1,639.08

Round.

S 1,639.1

The surface area of the cylinder is about 1,639.1 ft2.


9 4

Surface Area of Prisms, Cylinders, and Spheres

9-4

Course 2

Unlike the surface of a prism or a cylinder, the surface of a sphere cannot be flattened without stretching or shrinking.


9 4

Surface Area of Prisms, Cylinders, and Spheres

9-4

Course 2

Because the surface of a sphere cannot be flattened out, it is impossible to make a net for a sphere. However, there is an exact formula for the area of a sphere.


9 4

Surface Area of Prisms, Cylinders, and Spheres

9-4

Course 2

Additional Example 3: Finding the Surface Area of a Sphere

Find the surface area of the sphere to the nearest tenth. Use 3.14 for .

Use the formula.

S = 4r2

Substitute.

S  4 · 3.14 · 82

Multiply.

S  803.84

Round.

S  803.8

The surface area of the sphere is about 803.8 m2.


9 4

Surface Area of Prisms, Cylinders, and Spheres

9-4

Course 2

Try This: Example 3

Find the surface area of the sphere to the nearest tenth. Use 3.14 for .

Use the formula.

S = 4r2

6 in.

Substitute.

S  4 · 3.14 · 62

Multiply.

S  452.16

Round.

S  452.2

The surface area of the sphere is about 452.2 in2.


9 4

Surface Area of Prisms, Cylinders, and Spheres

9-4

Course 2

Insert Lesson Title Here

Lesson Quiz

Find the surface area of each figure to the nearest tenth.

3. a sphere with radius 6 ft

1.

2.

100.5 ft2

352.0 ft2

452.2 ft2

4. A drum is closed on the top and the bottom. The diameter of the drum is 18 in. The height is 32 in. Find the surface area.

2,317.3 in2


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