johmat


 * joma616 chapter 9 link

7.1)** **Surface Area and Volume** Altitude-** is a segment that has endpoints in the planes containing the bases and that is perpendicular to both planes.
 * objectives**-
 * 1) Explore ratio of surface area to volume.
 * 2) Develop the concepts of maximizing volume and minimizing the surface area
 * Definitions:
 * Height-** is the lenght of an altitude.

S=2LW+2WH+2LH and V = LWH S= 6s squared and V=s3 7.2) Surface Area and Volume of Prisms
 * Suface Area and Volume Formulas:**

If the length of a rectangular prism is 4, the height 6, and the width 2. Using the formulas above, find the surface area and volume.
 * Example**

S = 2(4)(2) + 2(4)(6) + 2(2)(6) S = 16 + 48 + 24 S = 88 V = lwh V = (4)(2)(6) V = 48

3**.** Use Cavalieri's Priniciple to develope a formula for the of a right or oblique prism
 * 7.2) Surface Area and Volume of Prisms objectives-**
 * 1) Define and use a formula for finding the suface area of a right prism
 * 2) Define and use a formula for finding the volume of a right prism

S=L+2B or S= HP + 2B
 * Surface Area of a Right Prism:**


 * Cavalieri's Principle-** If two solids have equal heights and the cross sections formed by every plane parallel to the base of both solid have equal areas, then the two solids have equal volumes.

V=BH
 * Volume of a Prism:**

objectives-** Define and use a formula for the surface area of a regular pyraimd Define and use a formula for the volume of a pyramid
 * 7.3) Surface Area and Volume of Pyramids

Pyramid-** A polyhedron in which all but one of the polygonal faces intersect at a single point known as the vertex of the pyramid. Find the surface area of a regular square pyramid whose slant height is //l// and whose base edge is //s.//
 * Definitions:
 * Base-** The bottom and top of a structure.
 * Lateral face-** The faces of a prism or pyramid that are not bases.
 * Vertex of the pyramid-** The lateral faces are triangles that share a single vertex.
 * Base Edge-** Each lateral faces are triangles that share a single vertex.
 * Lateral edge-** The intersection of two lateral faces of a polyhedron.
 * Altitude-** The perpendicular segment from the vertex to the plane of the base.
 * Height-** The length of an altitude of a polygon.
 * Regular pyramid-** A pyramid whose base is a regular polygon and whose lateral faces are congruent.
 * Slant height-** In a regular pyramid, the length of an altitude of a lateral face
 * __Example 1.__**

S= L + B S=4 (1/2sl) + s^2 ~ This can be written as follows: S= 1/2 L (4s) + s^2...because 4s is the perimeter of the base. S= 1/2 lp + s^2

S= L+B or S= 1/2 LP+B
 * Surface Area of a Regular Pyramid-**

V = 1/3 BH
 * Volume of a Pyramid-**

Objectives:** 1.Define and use the formula for the surface area of a rigt cylinder 2. Define and use a formula for the volume of a cylinder.
 * 7.4) Surface Area and Volume of Cylinders

S= L+B or S=2(pi)rh+2(pi)r^2
 * Definitions:**
 * Cylinder-** is a solid that consists of a circular region and its translted image on a parallel plane.
 * Lateral Surface-** the curved surface of a cylinder or cone.
 * Altitude-** of a cylinder is a segment that has endpoint in the planes containing the bases and is perpendicular or both planes.
 * Height-** lenght of an altitude
 * Axis-** of a cylinder is the segment joining the centers of the two bases.
 * Right Cylinder-** a cylinder whose axis is perpendicular to the base.
 * Oblique Cylinder-** a cylinder that is not a right cylinder.
 * Surface Area of a Right Cylinder.**

V=Bh or V=(3.14)r^2h
 * volume of a cylinder:**

estimate the surface area of the penny. S=2(pi)rh+2(pi)r^2 S=2(pi)(9.525)(1.55)+2(pi)(9.525)^2 ~663.46 square mm
 * Example:** A penny is a right sylinder with a diameter of 19.05 mm and a thicknoss of 1.55 mm. Ignoring the design,
 * Solution:** The radius of a penny is half of the diameter, of 90525 mm. Use the formula for teh SA of a right cylinder.

Objectives:** 1.Define and use the formula for the surface area of a cone. 2.Define and use the formula for the volume of a cone.
 * 7.5) Surface Area and Volume of Cone

Cone-** A three dimensional figure that consists of a circular base and a curved lateral surface that connects the base to the base. S= L+B or S= (pi)RL + (pi)R2
 * Definitions:
 * Base-** The circular face of a cone.
 * Lateral surface-** The curved surface of a cylinder that are not bases.
 * Altitude-** A segment from the vertex perpendicular to the plane of the base.
 * Height-** The length of an altitude of a polygon.
 * Right Cone-** A cone in which the altitude intersects the base at its center point.
 * Oblique Cone-** A cone that is not a right cone.
 * Slant Height of a cone-** The length of an altitude of a lateral face.
 * Surface Area of a Right Cone:**

V= 1/3BH or V= 1/3(pi)R2H
 * Volume of a Cone:**

Objectives:** Define and use the formula for the surface area of a sphere. Define and use the formula for the volume of a sphere.
 * 7.6) Surface Area and Volume of Spheres

Sphere-** is the set of all points in space that are the same distance from a given point known as the center of the sphere. V= 4/3(pi)R3
 * Definitions:
 * Volume of a Sphere:**

S= 4(pi)R
 * Surface Area of a Sphere:**

Objectives:** Define various transformations in three-dimensional space. Solve problems by using transformations in three-dimensional space.
 * 7.7) Three-Dimensional Symmetry-

first take the radius, it should be given, and plug it into the formula 4(pi)r^2 so lets say the radius was 2 it would be 4(pi)2^1 which turns out to be approx.50.27
 * Example**

1. Volume of a Trianular Prism 2. Surface Area of a Triangular Prism 3. Volume of a Pyramid 4. Surface Area of a Pyramid 5. Volume of a Cylinder 6. Surface Area of a Cylinder 7. Volume of a Cone 8. Surface Area of a Cone 9. Volume of a Sphere 10. Surface Area of a Sphere
 * BH**
 * L+2B or HP+2B**
 * (1/3)BH**
 * L+B or (1/2)//l//P+B**
 * BH or (pi)r//²// h**
 * L+2B or 2(pi)rh + 2(pi)r²**
 * (1/3)BH or (1/3)(pi)r//²// h**
 * L+B or (pi)r//l// + (pi)r//²//**
 * (4/3)(pi)r³**
 * 4(pi)r//²e//**