9-4 Surface Areas of Prisms, Cylinders,

and Spheres

Course 2

Warm Up

Problem of the Day

Lesson Presentation

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

12.6 ft3

33.5 ft3

162 ft3

2. cone with radius 2 ft and height 3 ft

3. sphere with diameter 4 ft

4. triangular pyramid with base 54 ft2 and height 9 ft

Course 2

9-4 Surface Area of Prisms, Cylinders, and

Spheres

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

Course 2

9-4 Surface Area of Prisms, Cylinders, and

Spheres

Learn to find the surface area of prisms,

cylinders, and spheres.

Course 2

9-4 Surface Area of Prisms, Cylinders, and

Spheres

Vocabulary

net

surface area

Insert Lesson Title Here

Course 2

9-4 Surface Area of Prisms, Cylinders, and

Spheres

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.

Course 2

9-4 Surface Area of Prisms, Cylinders, and

Spheres

SURFACE AREA OF A POLYHEDRON

The surface area of a polyhedron is found by adding the areas of each face of the polyhedron.

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.

Course 2

9-4 Surface Area of Prisms, Cylinders, and

Spheres

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,

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

= 2lw + 2lh + 2wh Top

Bottom

Front Back

Left Right w

h

l

Course 2

9-4 Surface Area of Prisms, Cylinders, and

Spheres

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

Additional Example 1: Finding the Surface Area of a

Prism

= 2lw + 2lh + 2wh S

= (2 · 15 · 9) + (2 · 15 · 7) + (2 · 9 · 7) S Substitute.

S = 270 + 210 + 126

S = 606

The surface area of the prism is 606 in2.

Multiply.

Add.

Course 2

9-4 Surface Area of Prisms, Cylinders, and

Spheres

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

= 2lw + 2lh + 2wh S

= (2 · 4 · 6) + (2 · 4 · 3) + (2 · 6 · 3) S Substitute.

S = 48 + 24 + 36

S = 108

The surface area of the prism is 108 in2.

Multiply.

Add.

Try This: Example 1

4 in.

6 in.

3 in. 3 in.

Course 2

9-4 Surface Area of Prisms, Cylinders, and

Spheres

4 in.

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, 2r, of the cylinder. So the area of the lateral surface is 2r. The area of each base is r2.

r Circumference of cylinder (2r)

h

Course 2

9-4 Surface Area of Prisms, Cylinders, and

Spheres

SURFACE AREA OF A CYLINDER

The surface area S of a cylinder is the sum of the areas of its bases, 2r2, plus the area of its lateral surface, 2rh.

S= 2r2 + 2rh

Course 2

9-4 Surface Area of Prisms, Cylinders, and

Spheres

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

Additional Example 2: Finding the Surface Area of a

Cylinder

6 ft

6 ft

8.3 ft

S = 2r2 + 2rh

S (2 · 3.14 · 62) + (2 · 3.14 · 6 · 8.3) Substitute.

Use the formula.

S 226.08 + 312.744

S 538.824

S 538.8

The surface area of the cylinder is about 538.8 ft2.

Multiply.

Add.

Round.

Course 2

9-4 Surface Area of Prisms, Cylinders, and

Spheres

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

9 ft

9 ft

20 ft

S = 2r2 + 2rh

S (2 · 3.14 · 92) + (2 · 3.14 · 9 · 20) Substitute.

Use the formula.

S 508.68 + 1130.4

S 1,639.08

S 1,639.1

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

Multiply.

Add.

Round.

Try This: Example 2

Course 2

9-4 Surface Area of Prisms, Cylinders, and

Spheres

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

Course 2

9-4 Surface Area of Prisms, Cylinders, and

Spheres

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.

SURFACE AREA OF A SPHERE

The surface area S of a sphere is 4 times times the radius r squared.

S= 4r2

Course 2

9-4 Surface Area of Prisms, Cylinders, and

Spheres

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

Additional Example 3: Finding the Surface Area of a

Sphere

S = 4r2

S 4 · 3.14 · 82

S 803.84

S 803.8

The surface area of the sphere is about 803.8 m2.

Use the formula.

Substitute.

Multiply.

Round.

Course 2

9-4 Surface Area of Prisms, Cylinders, and

Spheres

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

S = 4r2

S 4 · 3.14 · 62

S 452.16

S 452.2

The surface area of the sphere is about 452.2 in2.

Use the formula.

Substitute.

Multiply.

Round.

Try This: Example 3

6 in.

Course 2

9-4 Surface Area of Prisms, Cylinders, and

Spheres

Lesson Quiz

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

3. a sphere with radius 6 ft

100.5 ft2 352.0 ft2

Insert Lesson Title Here

452.2 ft2

2,317.3 in2

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.

1. 2.

Course 2

9-4 Surface Area of Prisms, Cylinders, and

Spheres