Pre Algebra Periods 1, 2, & 4

Space Figures 10-4 (solids)
SPACE FIGURES OR SOLIDS OR 3 DIMENSIONAL FIGURES

prisms = 2 congruent parallel bases - all other sides are rectangles
cylinder = 2 congruent circle bases
When you remove one base from a prism, it becomes a pyramid - all other sides are triangles
When you remove one base from a cylinder, it becomes a cone
When you have a set of points in all directions that are equal distance from a central point, you have a sphere
Vertices - the points where edges connect (the corners)
Edges - the line segments that connect the vertices

You should be able to visualize what a figure will look like if you could cut it apart and open it—that is called a net

SURFACE AREA OF CYLINDERS & PRISMS 10-5
Surface area is just the sum of the areas of all the sides

SHORTCUT TO ADDING UP ALL THE SIDES:
Just find the perimeter of ONE base and then multiply that by the height of the prism
Add to that the areas of the TWO bases, and you'll have the surface area
S.A. = area of 2 bases + (perimeter of one base)(height of prism)

According to our textbook:

the perimeter of one base X height = LATERAL AREA (L.A.)

the area of the base (base X height) = B

so

S.A. = L.A. + 2B
For a cylinder, do the same exact thing except now it's the CIRCUMFERENCE of the base
S.A. = area of the 2 bases + (circumference of one base)(height of cylinder)

S.A. OF PYRAMIDS, CONES, AND SPHERES
PYRAMIDS 10-6
For pyramids, you can simply add up the areas of all the sides
S.A. = area of 1 base + lateral areas (sides)
Lateral areas are all triangles in a pyramid and A = 1/2 bh
This time the height means the height of the triangle that is a side. It has a special name = slant height
The slant height is denoted as a cursive l

so S.A. = area of base + (1/2 bl)(# of sides)

CONES
For cones, you have one circle base plus a sort of triangular piece with the base being rounded
The cursive l now stands for the length of the slant side of this piece

S.A. = area of the circle + (pi)(radius of base)(slant height)
S.A. = (pi)r² + (pi)rl [pronounce this pie roll!)

SPHERES
S.A. + 4(pi)r²
(I always thought of this as you need 4 circles to wrap the basketball!)