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=This page is going to teach you about Surface Area and Volume for solid figures.= ==

Section 1: Surface Area and Volume
[|Surface area and volume for solid figures] __**Objectives**__
 * Develop the concepts of maximizing volume and minimizing surface area


 * Surface area** is the total area of all exposed surfaces of an object.
 * Volume** is the number of cubes that will fill the interior of an object.


 * __Surface Area and Volume Formulas__**

Surface area and volume formula for a rectangular prism is S= 2LW+2WH+2LH and V= LWH S- surface area V- volume L- length W- width H- height

Surface area and volume formula for a cube is S= 6s² and V= s³ S- surface area V- volume s= sides

**__Section 2: Surface Area and Volume of Prisms__**

 * __Objectives__**
 * Define and use a formula for finding the surface area of a right prism
 * Define and use a formula for finding the volume of a right prism
 * Use Cavalieri's Principle to develop a formula for the volume of a right or oblique prism

An **altitude** of a prism is a segment that has endpoints in the planes containing the bases and that is perpendicular to both planes. The **height** of a prism is the length of an altitude.

The surface area, S, of a right prism with lateral area L, base area B, perimeter p, and height h is: S= L+2B or S= hp+2B
 * __Surface Area of a Right Prism__**


 * __Volumes of Oblique Prisms__**

Calvalieri's Principle: If two solids have equal heights and the cross sections formed by every plane parallel to the bases of both solides have equal areas, then the two solids have equal volume.

Volume of a Prism: The volume, V, of a prism with height h and base area B is: V= Bh

**__Section 3: Surface Area and Volume of Pyramids__**
Link to Surface area of [|cones and pyramids]

__**Objectives**__
 * Define and use a formula for the surface area of a regular pyramid
 * Define and use a formula for the volume of a pyramid

The **altitude** of a pyramid is the perpendicular segment from the vertex to the plane of the base. The **height** is the lenght of the pyramid.
 * __Pyramids__**

A **regular pyramid** all the lateral faces are congruent and altitudes meet at the base. The **slant height** of the pyramid is the length of a lateral face.

pyramids are named based on how their base is shaped
 * __Four Types of Pyramids__**
 * Triangle Pyramid
 * Rectangular Pyramid
 * Pentagonal Pyramid
 * Hexagonal Pyramid

½ lp is equal to the lateral area of regular pyramids. To find the surface area simply add the base area to that formula.
 * __Surface Area of a Pyramid__**

The surface area, S, of a regular pyramid with lateral area L, base area B, perimeter of the base p, and slant height l is: S= L+B or S= ½ lp+B

The volume, V, of a pyramid with height h and base area B is: V=1/3 Bh
 * __Volume of a Pyramid__**

= =

**__Section 4: Surface Area and Volume of Cylinders__**
[|Surface Area and Volume of Cylinders]
 * __Objectives__**
 * Define and use a formula for the surface are of a right cylinder
 * Define and use a formula for the volume of a cylinder

__**Cylinder**__ A **cylinder** is a solid that consists of a circular region and its translated image on a parallel plane The **axis** of the cylinder connects the center of the two bases together
 * Lateral surface** is what connects the two circles
 * Bases** of the cylinder are the faces that are formed by the circular region


 * __Two Types of Cylinders__**
 * Right Cylinder** is when the cylinder is perpendicular to the bases
 * Oblique Cylinder** is when they are not perpendicular to the bases

__**Surface Area of a Right Cylinder**__ The surface are, S, of a right cylinder with lateral area L, base area B, radius r, and height h is: S= L+2B Example:

The volume, V, of a cylinder with radius r, height h, and base area B is: V= Bh Find the volume of a can of pop when the base is 3 inches and the height is 6 inches V= 3*6 = 18 inches³
 * __Volume of Cylinders__**
 * Example:**

__**Section 5: Surface Area and Volume of Cones**__
[|Surface Area and Volume of Cones] __**Objectives**__
 * Define and use the formula for the surface area of a cone.
 * Define and use the formula for the volume of a cone.

__**Cones**__ A **cone** is a three dimentional figure that consists of a circular **base** and a curve **lateral surface** that connects the base to a single point not in the plane of the base, called the **vertex**.


 * Altitude** of a cone is the perpendicular line from the vertex.
 * Height** of a cone is the length of the altitude.


 * __Two Types of Cones__**
 * Right cone** is if the altitude intersects the center of the base.
 * Oblique cone** is if the altitude doesn't intersect the center of the base.

The surface area, S, of a right cone with lateral area L, base of area B, radius r, and slant height l is: S= L+B What is the surface area of the right cone when the lateral area L, is 30 and the base of area B, is 15. S= 30+15 = 45 units²
 * __Surface Area of a Right Cone__**
 * Example:**

The volume, V, of a cone with radius r, height h, and base area B is: V= 1/3Bh A cone in the street is 2 feet tall and the base is 1 foot. Find the volume of the cone V= 1/3*1*2= .66 cubic feet
 * __Volume of a Cone__**
 * Example:**

**__Section 6: Surface Area and Volume of Spheres__**

 * __Objectives__**
 * Define and use the formula for the surface area of a sphere
 * Define and use the formula for the volume of a sphere

The volume, V, of a sphere with the radius r is: V= 4/3πr³ Find the volume of an exercise ball when the radius is 1½ feet. V= 4/3π(1½)³ =14.1 cubic feet The surface area, S, of a sphere with radius r is: S= 4πr² Find the surface area of a clock when the radius is 3 feet. S= 4π(3)² = 113 squared feet
 * __Volume of a Sphere__**
 * Example:**
 * __Surface Area of a Sphere__**
 * Example:**

__**Section 7: Three-Dimensional Symmetry**__

 * __Objectives__**
 * Define various transformations in three-dimensional space
 * Solve problems by using transformations in three-dimentsional space

Three dimensionals can be reflected across a line.
 * __Three-Dimensional Reflections__**