SECTION 12-2 SURFACE AREAS OF PRISMS AND CYLINDERS
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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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