SECTION 12-2SURFACE AREAS OF PRISMS AND CYLINDERS

ESSENTIAL QUESTIONS

• How do you find lateral areas and surface areas of prisms?

• How do you find lateral areas and surface areas of cylinders?

VOCABULARY1. Lateral Face:

2. Lateral Edge:

3. Base Edge:

4. Altitude:

VOCABULARY1. Lateral Face:

2. Lateral Edge:

3. Base Edge:

4. Altitude:

The surfaces of a polyhedron that are not bases

VOCABULARY1. Lateral Face:

2. Lateral Edge:

3. Base Edge:

4. Altitude:

The surfaces of a polyhedron that are not bases Formed where the lateral faces intersect

VOCABULARY1. Lateral Face:

2. Lateral Edge:

3. Base Edge:

4. Altitude:

The surfaces of a polyhedron that are not bases Formed where the lateral faces intersect

Formed where the lateral faces intersect the base(s)

VOCABULARY1. Lateral Face:

2. Lateral Edge:

3. Base Edge:

4. Altitude:

The surfaces of a polyhedron that are not bases Formed where the lateral faces intersect

Formed where the lateral faces intersect the base(s)

The perpendicular segment that joins the bases of a prism/cylinder

VOCABULARY5. Height:

6: Lateral Area:

7. Axis:

VOCABULARY5. Height:

6: Lateral Area:

7. Axis:

Another word for the altitude of a prism/cylinder

VOCABULARY5. Height:

6: Lateral Area:

7. Axis:

Another word for the altitude of a prism/cylinder The sum of the areas of the lateral faces

VOCABULARY5. Height:

6: Lateral Area:

7. Axis:

Another word for the altitude of a prism/cylinder The sum of the areas of the lateral faces

In a cylinder, this is the segment whose endpoints are the centers of the circular bases

PARTS OF A PRISM

PARTS OF A PRISMLateral Face

PARTS OF A PRISMLateral Face

PARTS OF A PRISMLateral FaceLateral Edge

PARTS OF A PRISMLateral FaceLateral Edge

PARTS OF A PRISMLateral FaceLateral Edge

Bases

PARTS OF A PRISMLateral FaceLateral Edge

Bases

PARTS OF A PRISMLateral FaceLateral Edge

Base EdgeBases

PARTS OF A PRISMLateral FaceLateral Edge

Base EdgeBases

PARTS OF A PRISMLateral FaceLateral Edge

Base EdgeAltitude/Height

Bases

LATERAL AREA OF A PRISM

LATERAL AREA OF A PRISM

L = Ph

LATERAL AREA OF A PRISM

L = Lateral Area

L = Ph

LATERAL AREA OF A PRISM

L = Lateral Area

P = Perimeter of the Base

L = Ph

LATERAL AREA OF A PRISM

L = Lateral Area

P = Perimeter of the Base

h = Height of the Prism

L = Ph

EXAMPLE 1Find the lateral area of the regular hexagonal prism.

EXAMPLE 1Find the lateral area of the regular hexagonal prism.

L = Ph

EXAMPLE 1Find the lateral area of the regular hexagonal prism.

L = Ph

P = 5(6)

EXAMPLE 1Find the lateral area of the regular hexagonal prism.

L = Ph

P = 5(6) = 30 cm

EXAMPLE 1Find the lateral area of the regular hexagonal prism.

L = Ph

P = 5(6) = 30 cm

L = 30(12)

EXAMPLE 1Find the lateral area of the regular hexagonal prism.

L = Ph

P = 5(6) = 30 cm

L = 30(12) = 360 cm2

SURFACE AREA OF A PRISM

SURFACE AREA OF A PRISM

SA = L + 2B or SA= Ph + 2B

SURFACE AREA OF A PRISM

L = Lateral Area

SA = L + 2B or SA= Ph + 2B

SURFACE AREA OF A PRISM

L = Lateral Area

P = Perimeter of the Base

SA = L + 2B or SA= Ph + 2B

SURFACE AREA OF A PRISM

L = Lateral Area

P = Perimeter of the Base

SA = L + 2B or SA= Ph + 2B

B = Area of the Base

SURFACE AREA OF A PRISM

L = Lateral Area

P = Perimeter of the Base

h = height of the prism

SA = L + 2B or SA= Ph + 2B

B = Area of the Base

EXAMPLE 2Find the surface area of the rectangular prism.

EXAMPLE 2Find the surface area of the rectangular prism.

SA = L + 2B

EXAMPLE 2Find the surface area of the rectangular prism.

SA = 4(6)(10) + 2(6)(6)

SA = L + 2B

EXAMPLE 2Find the surface area of the rectangular prism.

SA = 4(6)(10) + 2(6)(6)

SA = 312 in2

SA = L + 2B

PARTS OF A CYLINDER

PARTS OF A CYLINDERBases

PARTS OF A CYLINDERBases

PARTS OF A CYLINDERBasesAxis

PARTS OF A CYLINDERBasesAxis

PARTS OF A CYLINDERBasesAxis

Altitude/Height

LATERAL AREA OF A CYLINDER

LATERAL AREA OF A CYLINDER

L = 2πrh

LATERAL AREA OF A CYLINDER

L = Lateral Area

L = 2πrh

LATERAL AREA OF A CYLINDER

L = Lateral Area

r = Radius of the Base

L = 2πrh

LATERAL AREA OF A CYLINDER

L = Lateral Area

r = Radius of the Base

h = Height of the Cylinder

L = 2πrh

SURFACE AREA OF A CYLINDER

SURFACE AREA OF A CYLINDER

SA = L + 2B or SA = 2πrh + 2πr2

SURFACE AREA OF A CYLINDER

L = Lateral Area

SA = L + 2B or SA = 2πrh + 2πr2

SURFACE AREA OF A CYLINDER

L = Lateral Area

SA = L + 2B or SA = 2πrh + 2πr2

B = Area of the Base

SURFACE AREA OF A CYLINDER

L = Lateral Area

r = Radius of the Base

SA = L + 2B or SA = 2πrh + 2πr2

B = Area of the Base

SURFACE AREA OF A CYLINDER

L = Lateral Area

r = Radius of the Base

h = Height of the Cylinder

SA = L + 2B or SA = 2πrh + 2πr2

B = Area of the Base

EXAMPLE 3Find the lateral area and the surface area of the cylinder. Round to the nearest hundredth.

EXAMPLE 3Find the lateral area and the surface area of the cylinder. Round to the nearest hundredth.

L = 2πrh

EXAMPLE 3Find the lateral area and the surface area of the cylinder. Round to the nearest hundredth.

L = 2πrhL = 2π (14)(18)

EXAMPLE 3Find the lateral area and the surface area of the cylinder. Round to the nearest hundredth.

L = 2πrhL = 2π (14)(18)

L ≈ 1583.36 ft2

EXAMPLE 3Find the lateral area and the surface area of the cylinder. Round to the nearest hundredth.

EXAMPLE 3Find the lateral area and the surface area of the cylinder. Round to the nearest hundredth.

SA = L + 2B

EXAMPLE 3Find the lateral area and the surface area of the cylinder. Round to the nearest hundredth.

SA = L + 2BSA = 2πrh + 2πr2

EXAMPLE 3Find the lateral area and the surface area of the cylinder. Round to the nearest hundredth.

SA = L + 2B

SA = 2π (14)(18) + 2π (14)2SA = 2πrh + 2πr2

EXAMPLE 3Find the lateral area and the surface area of the cylinder. Round to the nearest hundredth.

SA = L + 2B

SA = 2π (14)(18) + 2π (14)2SA = 504π + 392π

SA = 2πrh + 2πr2

EXAMPLE 3Find the lateral area and the surface area of the cylinder. Round to the nearest hundredth.

SA = L + 2B

SA = 2π (14)(18) + 2π (14)2SA = 504π + 392π

SA = 896π

SA = 2πrh + 2πr2

EXAMPLE 3Find the lateral area and the surface area of the cylinder. Round to the nearest hundredth.

SA = L + 2B

SA = 2π (14)(18) + 2π (14)2SA = 504π + 392π

SA = 896π ≈ 2814.87 ft2

SA = 2πrh + 2πr2

PROBLEM SET

PROBLEM SET

p. 833 #1-23 odd

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