1. Lateral Area, Surface Area, and Volume
Honors Geometry
Unit 8
Prisms and Cylinders
Lesson 2
Lateral Area, Surface Area, and Volume

2. Lesson 10-2: 3-D Views of Solid Figures
Different Views
Perspective view of a cone
Different angle views of a cone
the side
(or from any side view)
the top
the bottom
Lesson 10-2: 3-D Views of Solid Figures

3. Example: Different Views
Front
Left
Right
Back
Top
* Note: The dark lines indicated a break in the surface.
Lesson 10-2: 3-D Views of Solid Figures

4. Lesson 10-2: 3-D Views of Solid Figures
Sketches
Sketch a rectangular solid 7 units long, 4 units wide, and 3 units high using Isometric dot paper .
Step 1: Draw the top of a solid 4 by 7 units.
Lesson 10-2: 3-D Views of Solid Figures

5. Lesson 10-2: 3-D Views of Solid Figures
Sketches - continued
Step 2: Draw segments 3 units down from each vertex (show hidden sides with dotted lines).
Lesson 10-2: 3-D Views of Solid Figures

6. Lesson 10-2: 3-D Views of Solid Figures
Sketches - continued
Step 3: Connect the lower vertices. Shade the top of the figure for depth if desired. You have created a corner view of the solid figure.
Lesson 10-2: 3-D Views of Solid Figures

7. Lesson 10-2: 3-D Views of Solid Figures
Nets and Surface Area
Imagine cutting a cardboard box along its edges and laying it out flat. The resulting figure is called a net.
top
back
end
front
bottom =
A net is very helpful in finding the surface area of a solid figure.
Lesson 10-2: 3-D Views of Solid Figures

8. Let’s look at another net.
This is a triangular pyramid.
Notice that all sides lay out to be triangles. =
Lesson 10-2: 3-D Views of Solid Figures

9. Find the surface area of the figure using a net.
First, imagine the figure represented as a net.
Find the area of each face.
Find the sum of all the individual areas.
33 10 6 6 10
33 =
Surface area =
(6 x 10) + (6 x 10) + (6 x 10) + ½(6)(33) + ½ (6)(33) =
3 + 93 = 3
Lesson 10-2: 3-D Views of Solid Figures

10. lateral face – not base
lateral edge – intersections of lateral faces, all parallel and congruent
base edge – intersection of lateral face and base
Altitude - perpendicular segment between bases
Height – length of the altitude
lateral area – sum of areas of all lateral faces

11. Prism Lateral Area of a Prism LA = Ph Surface Area : SA = Ph + 2B
= [Lateral Area + 2 (area of the base)]
Volume of a Right Prism (V )= Bh
(P = perimeter of the base, h = height of prism, B = base area) h
Triangular Prism h

12. Find the lateral area of the regular hexagonal prism.
Lateral Area of a Prism
Find the lateral area of the regular hexagonal prism.
The bases are regular hexagons. So the perimeter of one base is 6(5) or 30 centimeters.
Lateral area of a prism
P = 30, h = 12
Multiply.
Answer: The lateral area is 360 square centimeters.

13. Find the lateral area of the regular octagonal prism.
A. 162 cm2
B. 216 cm2
C. 324 cm2
D. 432 cm2

14. Find the surface area of the rectangular prism.
Surface Area of a Prism
Find the surface area of the rectangular prism.

15. Answer: The surface area is 360 square centimeters.
Surface Area of a Prism
Surface area of a prism
L = Ph
Substitution
Simplify.
Answer: The surface area is 360 square centimeters.

16. Find the surface area of the triangular prism.
A. 320 units2
B. 512 units2
C. 368 units2
D. 416 units2

17. Find the volume of the prism.
Volume of a Prism
Find the volume of the prism.
V Bh Volume of a prism
1500 Simplify.
Answer: The volume of the prism is 1500 cubic centimeters.

18. Find the volume of the prism.
A in3
B in3
C in3
D in3

19. Examples: 5 4 8 h = 8 h = 4 B = 5 x 4 = 20 B = ½ (6)(4) = 12
perimeter of base = 2(5) + 2(4) = 18
perimeter of base = = 19
L. A.= 18 x 8 = 144 sq. units
L. A. = 19 x 4 = 76 sq. units
S.A. = (20) = 184 sq. units
S. A. = (12) = 100 sq. units
V = 20 x 8 = 160 cubic units
V = 12 x 4 = 48 cubic units

20. Prisms A and B have the same width and height, but different lengths
Prisms A and B have the same width and height, but different lengths. If the volume of Prism B is 128 cubic inches greater than the volume of Prism A, what is the length of each prism?
Prism B
Prism A
A 12 B 8
C 4 D 3.5

21. Read the Test Item
You know the volume of each solid and that the difference between their volumes is 128 cubic inches.
Solve the Test Item
Volume of Prism B –
Volume of Prism A = 128 Write an equation.
4x ● 9 – 4x ● 5 = 128 Use V = Bh.
16x = 128 Simplify.
x = 8 Divide each side by 16.
Answer: The length of each prism is 8 inches. The correct answer is B.

22. Examples: 5 4 8 h = 8 h = 4 B = 5 x 4 = 20 B = ½ (6)(4) = 12
perimeter of base = 2(5) + 2(4) = 18
perimeter of base = = 19
L. A.= 18 x 8 = 144 sq. units
L. A. = 19 x 4 = 76 sq. units
S.A. = (20) = 184 sq. units
S. A. = (12) = 100 sq. units
V = 20 x 8 = 160 cubic units
V = 12 x 4 = 48 cubic units

23. Cylinders Formulas: S.A. = 2πr ( r + h ) V =
Cylinders are right prisms with circular bases.
Therefore, the formulas for prisms can be used for cylinders.
Surface Area (SA) = 2B + LA = 2πr ( r + h )
The base area is the area of the circle:
The lateral area is the area of the rectangle: 2πrh
Volume (V) = Bh = h
2πr h

24. L = 2rh Lateral area of a cylinder
Lateral Area and Surface Area of a Cylinder
Find the lateral area and the surface area of the cylinder. Round to the nearest tenth.
L = 2rh Lateral area of a cylinder
= 2(14)(18) Replace r with 14 and h with 18.
≈ Use a calculator.

25. S = 2rh + 2r2 Surface area of a cylinder
≈ (14)2 Replace 2rh with and r with 14.
≈ Use a calculator.
Answer: The lateral area is about square feet and the surface area is about square feet.

26. Find the lateral area and the surface area of the cylinder
Find the lateral area and the surface area of the cylinder. Round to the nearest tenth.
A. lateral area ≈ 1508 ft2 and surface area ≈ ft2
B. lateral area ≈ 1508 ft2 and surface area ≈ ft2
C. lateral area ≈ 754 ft2 and surface area ≈ ft2
D. lateral area ≈ 754 ft2 and surface area ≈ ft2

27. L = 2rh Lateral area of a cylinder
Find Missing Dimensions
MANUFACTURING A soup can is covered with the label shown. What is the radius of the soup can?
L = 2rh Lateral area of a cylinder
125.6 = 2r(8) Replace L with 15.7 ● and h with 8.
125.6 = 16r Simplify.
2.5 ≈ r Divide each side by 16.
Answer: The radius of the soup can is about 2.5 inches.

28. Find the diameter of a base of a cylinder if the surface area is 480 square inches and the height is 8 inches.
A. 12 inches
B. 16 inches
C. 18 inches
D. 24 inches

29. Find the volume of the cylinder to the nearest tenth.
Volume of a Cylinder
Find the volume of the cylinder to the nearest tenth.
Volume of a cylinder
= (1.8)2(1.8) r = 1.8 and h = 1.8
≈ 18.3 Use a calculator.
Answer: The volume is approximately 18.3 cm3.

30. Find the volume of the cylinder to the nearest tenth.
A cm3
B cm3
C cm3
D cm3

31. Example
For the cylinder shown, find the lateral area , surface area and volume.
3 cm
S.A.= 2•πr2 + 2πr•h
L.A.= 2πr•h
4 cm
S.A.= 2•π(3)2 + 2π(3)•(4)
L.A.= 2π(3)•(4)
S.A.= 18π +24π
L.A.= 24π sq. cm.
S.A.= 42π sq. cm.
V = πr2•h
V = π(3)2•(4)
V = 36π