1. Lesson 12-x, 13-y
3D Figures Review

2. Objectives
Review 3-D Figures
Quiz on Friday
Ch Test after SOLs

3. Vocabulary
None new

4. Nets Cylinder Triangular Prism
Nets – cut a 3d figure on its edges and lay it flat. It can be folded into the shape of the 3d figure with no overlap h h r C
Square Prism (Cube)
Surface Area – Sum of each area of the faces of the solid

5. Spheres – Surface Area & Volume
Circles – Intersection between a plane and a sphere
Great Circles – Intersections between a plane passing through the center of the sphere and the sphere. Great circles have the same center as the sphere. The shortest distance between two points on a sphere lie on the great circle containing those two points.
Hemisphere – a congruent half of a sphere formed by a great circle. Surface areas of hemispheres are half of the SA of the sphere and the area of the great circle. Volumes of hemispheres are half of the volume of the sphere. r
V = 4/3 * π * r3
SA = 4π * r2
Sphere – All points equal distant from a center point in 3-space
V = 2/3 * π * r3
SA = 3π * r2

6. Cylinders – Surface Area & Volume
r – radius
h – height
Net h h C r
Volume (V) = B * h
Base Area (B) = π * r2
V = π * r2 * h
Surface Area = Lateral Area + Base(s) Area
LA = 2π * r * h = circumference * h
Bases Area = 2 * π * r2
SA = LA + BA
SA = 2π * r * h + 2π * r2

7. Prisms – Areas & Volumes
Regular Triangular Prism
Net
LA = 3 * b * l = Perimeter * l
Bases Area = 2* ½ * b * h
SA = LA + BA
SA = 3 * b * l + b * h b h b b l b
base perimeter
Surface Area (SA) – Sum of each area of (all) the faces of the solid
Lateral Area (LA) – Sum of each area of the non-base(s) faces of the solid
Surface Area = Lateral Area + Base(s) Area
Rectangular Prism
LA = 2 * w * h + 2 * L * h
Bases Area = 2 * L * w
SA = LA + BA
SA = 2(Lw + Lh + wh)
Volume (V) = B * h
Base Area (B) = L * w
V = L * w * h w h L

8. Cones – Surface Area & Volume
Net l
l – slant height
h – height h r
Surface Area = Lateral Area + Base(s) Area
Cone – A solid with circular base and a vertex.
LA = π * r * l
Base Area = π * r2
SA = LA + BA
SA = π * r * l + π * r2
Volume (V) = 1/3 * B * h
Base Area (B) = π * r2
V = 1/3 * π * r2 * h

9. Pyramids – Surface Area & Volume
Pyramid (Square) l h B l s
Net s
Surface Area = Lateral Area + Base(s) Area
l – slant height
½ perimeter
Volume (V) = 1/3 * B * h
Base area (B) = area of the base
example above V = 1/3 * s2 * h
LA = 4 * ½ s * l
Bases Area = s * s = s2
SA = LA + BA
SA = 2 * s * l + s2
In general: Pyramid LA = ½ P * l

10. Summary & Homework Summary: Homework:
Nets fold up into 3 dimensional figures
Formulas are on formula sheet
Must identify needed variables
Lateral surface area (LA) is the area of the sides
Base surface area (B) is the area of the top/bottom
Surface area = Lateral Area + Base(s) Area
Common Error: b is a length and B is an area
Homework:
study for Quiz