3sparya

=SECTION 1:=

-We are going to explore the ratios of surface area and volume. -We are going look into maximizing volume and minimizing surface area.


 * Surface Area and Volume Formulas:**

S=Surface Area. V=Volume. L=Length. W=Width. H= Height.

s=lw+2wh+2lh V=lwh

S=6s² and V=s³ = = =SECTION 2:= =[|Right prism]=

-We will use the formula for finding the surface area of a right prism. -We will use the formula for finding the volume of a right prism. -We are going cavalerie's principle for developing a formula for a right or oblique prism.

Altitude: How high an object or something is. Height: How tall an object or something is.
 * Vocabulary:**


 * Surface Area of a Right Prism:**

S=L+2B or S=hp+2B

S is surface area, L is the lateral area, B is the base area, P is the perimeter, and H is the height.


 * Cavalieri's Principle:**

If 2 solids have the same height and the sections that cross are formed by all the planes paralle to the bases of both solids. The 2 solids will then have equal volumes.


 * Volume of a Prism:**

V=Bh

V is volume, B is base and H is the height.

The formula reads Volume equals Base times Height.

=**Section 3: [|Regular pyramid]**=

-We will use the formula to find the surface area of a regular pyramid. -We will use the formula to find the volume of a pyramid.


 * Vocabulary:**

Pyramid: Has a base with 3 lateral faces. Base: Bottom of a polyhedron. Lateral faces: 3 or more make up a pyramid. Vertex of the pyramid: All lateral faces share 1 vertex. Base edge: Every face has an edge in relationship to the base. Lateral edge: Where 2 lateral faces intersect. Altitude: Intersects from the vertex to the bases plane. Height: The measure of the altitude. Regular pyramid: Lateral faces are isoceles triangles and the base is a polyhedron. Slant height: Measure of the altitude of any lateral face on a regular pyramid.


 * Surface Area of a Regular Pyramid:**

S is surface area, L is the lateral area, B is the base area, P is the perimeter and L is the slant height. S=L+B or S=½LP+B

V is the volume, H is the height and the base is B.
 * Volume of a Pyramid:**

V=1/3BH

= = =Section 4:= =[|Right cylinder]=

-We will use the formula to find the surface area of a right cylinder. -We will use the formula to find the volume of a cylinder.


 * Vocabulary:**

Cylinder: Has 2 bases with a circular tube enclosing it. Lateral surface: Connects the 2 bases to make a cylinder. Bases: Bottom and or top of a cylinder. Altitude: Has 2 endpoints from one base to the next base. Height: How long the altitude is. Axis: Joins the center of each of the bases together. Right cylinder: Axis are perpendicular to each other. Oblique cylinder: Axis aren't perpendicular to each other.


 * Surface Area of a Right Cylinder:**

Surface area is S, lateral area is L, base area is B, radius is R and the height is H.

S=L+2B or S=2πrh=2πr²


 * Volume of a Cylinder:**

Volume is V, radius is R, height is H and the base area is B.

V=BH or V=πr²h.

=Section 5:=

=**[|Cones]**=

-We will understand and use the formula for the surface area of a cone. -We will understand and use the formula for the volume of a cone.


 * Vocabulary:**

Cone: is 3 dimensional with a base that is a circle. Base: Bottom of a cone. Lateral surface: Connects base to a single point. Vertex: Connects the lateral surface to the base. Altitude: Perpendicular segment that connects the vertex to the plane. Height: How tall the altitude is. Right cone: Altitude of the cone meets the center of the base. Oblique cone: opposite of a right cone.


 * Surface area of a right cone:**

Surface area is S, lateral area is L, base area is B, radius is R and the slant height is L.

S=L+B or S=πRL+πR²


 * Volume of a cone:**

Volume is V, radius is R, height is H, base area is B.

V=1/3BH or V=1/3πR²H

=Section 6:=

=**[|Sphere]**= -We will use the formula to find the surface area of a sphere. -We will use the formula to find the volume of a sphere.


 * Vocabulary:**

Sphere: All points in space that are equal distance from the center of the sphere.


 * Volume of a sphere:**

Volume is V, and the radius is R.

V=4/3πR³


 * Surface area of a sphere:**

Surface area is S and the radius is R.

S=4πR²