1. Assignment
P : 2-20 even, 21, 24, 25, 28, 30
P : 2, 3-21 odd, 22-25, 30
Challenge Problems: 3-5, 8, 9

2. In Glorious 3-D!
Most of the figures you have worked with so far have been confined to a plane—two-dimensional. Solid figures in the “real world” have 3 dimensions: length, width, and height.

3. Polyhedron
A solid formed by polygons that enclose a single region of space is called a polyhedron.
Separate your Geosolids into 2 groups: Polyhedra and others.

4. Parts of Polyhedrons Polygonal region = face
Intersection of 2 faces = edge
Intersection of 3+ edges = vertex
face
edge
vertex

5. Warm-Up
Separate your Geosolid polyhedra into two groups where each of the groups have similar characteristics.
What are the names of these groups?
Prisms
Pyramids
Polyhedra:

6. 12.2 & 12.3: Surface Area of Prisms, Cylinders, Pyramids, and Cones
Objectives:
To find and use formulas for the lateral and total surface area of prisms, cylinders, pyramids, and cones

7. Prism
A polyhedron is a prism iff it has two congruent parallel bases and its lateral faces are parallelograms.

8. Classification of Prisms
Prisms are classified by their bases.

9. Right & Oblique Prisms
Prisms can be right or oblique. What differentiates the two?

10. Right & Oblique Prisms
In a right prism, the lateral edges are perpendicular to the base.

11. Pyramid
A polyhedron is a pyramid iff it has one base and its lateral faces are triangles with a common vertex.

12. Classification of Pyramids
Pyramids are also classified by their bases.

13. Pyramid
A regular pyramid is one whose base is a regular polygon.

14. Pyramid A regular pyramid is one whose base is a regular polygon.
The slant height is the height of one of the congruent lateral faces.

15. Solids of Revolution
The three-dimensional figure formed by spinning a two dimensional figure around an axis is called a solid of revolution.

16. Cylinder
A cylinder is a 3-D figure with two congruent and parallel circular bases.
Radius = radius of base

17. Cone
A cone is a 3-D figure with one circular base and a vertex not on the same plane as the base.
Altitude = perpendicular segment connecting vertex to the plane containing the base (length = height)

18. Cone
A cone is a 3-D figure with one circular base and a vertex not on the same plane as the base.
Slant height = segment connecting vertex to the circular edge of the base

19. Right vs. Oblique
What is the difference between a right and an oblique cone?

20. Right vs. Oblique
In a right cone, the segment connecting the vertex to the center of the base is perpendicular to the base.

21. Nets
Imagine cutting a 3-D solid along its edges and laying flat all of its surfaces. This 2-D figure is a net for that 3-D solid.
An unfolded pizza box is a net!

22. Nets
Imagine cutting a 3-D solid along its edges and laying flat all of its surfaces. This 2-D figure is a net for that 3-D solid.

23. Activity: Red, Rubbery Nets
Match one of the red, rubbery nets with its corresponding 3-D solid. Which of the shapes has no net?

24. Activity: Red, Rubbery Nets
A sphere doesn’t have a true net; it can only be approximated.
Match one of the red, rubbery nets with its corresponding 3-D solid. Which of the shapes has no net?

25. Exercise 1
There are generally two types of measurements associated with 3-D solids: surface area and volume. Which of these can be easily found using a shape’s net?

26. Surface Area
The surface area of a 3-D figure is the sum of the areas of all the faces or surfaces that enclose the solid.
Asking how much surface area a figure has is like asking how much wrapping paper it takes to cover it.

27. Lateral Surface Area
The lateral surface area of a 3-D figure is the sum of the areas of all the lateral faces of the solid.
Think of the lateral surface area as the size of a label that you could put on the figure.

28. Exercise 2 What solid corresponds to the net below?
How could you find the lateral and total surface area?

29. Exercise 3 Draw a net for the rectangular prism below. A B C D
To find the lateral surface area, you could:
Add up the areas of the lateral rectangles

30. Exercise 3 Draw a net for the rectangular prism below.
Height of Prism
Perimeter of the Base
To find the lateral surface area, you could:
Find the area of the lateral surface as one, big rectangle

31. Exercise 3 Draw a net for the rectangular prism below.
Height of Prism
Perimeter of the Base
To find the total surface area, you could:
Find the lateral surface area then add the two bases

32. Surface Area of a Prism Lateral Surface Area of a Prism:
P = perimeter of the base
h = height of the prism
Total Surface Area of a Prism:
B = area of the base

33. Exercise 4
Find the lateral and total surface area.

34. Exercise 5 Draw a net for the cylinder.
Notice that the lateral surface of a cylinder is also a rectangle. Its height is the height of the cylinder, and the base is the circumference of the base.

35. Exercise 6
Write formulas for the lateral and total surface area of a cylinder.

36. Surface Area of a Cylinder
Lateral Surface Area of a Cylinder:
C = circumference of base
r = radius of base
h = height of the cylinder
Total Surface Area of a Cylinder:

37. Exercise 7
The net can be folded to form a cylinder. What is the approximate lateral and total surface area of the cylinder?

38. Height vs. Slant Height
By convention, h represents height and l represents slant height.

39. Height vs. Slant Height
By convention, h represents height and l represents slant height.

40. Exercise 8 Draw a net for the square pyramid below.
To find the lateral surface area:
Find the area of one triangle, then multiply by 4

41. Exercise 8 Draw a net for the square pyramid below.
To find the lateral surface area:
Find the area of one triangle, then multiply by 4

42. Exercise 8 Draw a net for the square pyramid below.
To find the total surface area:
Just add the area of the base to the lateral area

43. Surface Area of a Pyramid
Lateral Surface Area of a Pyramid:
P = perimeter of the base
l = slant height of the pyramid
Total Surface Area of a Prism:
B = area of the base

44. Exercise 9
Find the lateral and total surface area.

45. Exercise 10
You may have realized that the formula for the lateral area for a prism and a cylinder are basically the same. The same is true for the formulas for a pyramid and a cone. Derive a formula for the lateral area of a cone.
Lateral area of a Pyramid:
Lateral area of a Cone:

46. Surface Area of a Cone Lateral Surface Area of a Cone:
r = radius of the base
l = slant height of the cone
Total Surface Area of a Cone:

47. Exercise 11
A traffic cone can be approximated by a right cone with radius 5.7 inches and height 18 inches. To the nearest tenth of a square inch, find the approximate lateral area of the traffic cone.

48. Tons of Formulas?
Really there’s just two formulas, one for prisms/cylinders and one for pyramids/cones.

49. Assignment
P : 2-20 even, 21, 24, 25, 28, 30
P : 2, 3-21 odd, 22-25, 30
Challenge Problems: 3-5, 8, 9