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Chapter 7 7.1 Rectangular right prism S=2lw + 2wh + 2lh and V=lwh Cube S=6SSquared and V=SCubed
 * Objectives:** Explore ratios of surface area to volume and understand/develop concepts of maximizing volume and minimizing surface area.
 * Surface are and volume formulas:**

7.2 Define and use a formula for finding the volume of a right prism. Use Cavalieri’s Principle to develop a formula for a right or oblique prism.
 * Objectives:** Define and use a formula for finding the surface area of a prism.volume


 * Altitude:** of a prism is a segment that has endpoints in the planes containing the bases and that is perpendicular to both planes.


 * 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//**

7.3 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 Pyramid: is a polyerdron consisting of a base, is a polygon, and three or more lateral faces Altitude: Is a perpendicular segment from the vertex to the plane of a base.(in a pyramid) Height: Of a pyramid is the length of it's Altitude. Regular Pyramid: A pyramid whose base is a rgular polygon and whose lateral faces are congruent isoscles triangles. SURFACE AREA OF A REGULAR PYRAMID The surface area, S, of a regular pyramid with lateral area L, base area B, perimeter of te base p, and slant height of l, is S=L+B or S=1/2lp+B VOLUME OF A PYRAMID The volume, V, of a pyramid with height h, and base area B is V=1/3Bh

7.4 Objectives: Define and use a formula for the surface area of a right cylinder Define and use a formula for the volume of a cylinder Cylinder: is a Solid that consists of a circular region and it's translated image on a parallel plane, with a lateral surface connecting the circles. Altitude: of a cylinder is a segment that has endpoints in th planes containing the bases and is perpendicular to both planes Axis: of a Cylinder is the segment joining th centers of the two bases Right Cylinder: is a cylinder with an axis that is perpendicular to it's bases(oblique if it is not) SURFACE AREA OF A RIGHT CYLINDER The surface area S, of a right cylinder with lateral area L, base area B, radius r, and height h is S=L+2B or S=2(3.14)h+2(3.24)r(squared)

VOLUME OF A CYLINDER The volume, V, of a cylinder with radius r, height h, and base area B is V=Bh or V=3.14r(squared)h

7.5 Objectives: Define and use the formula for the surface area of a cone Define and use the formula for the volume of a cone Cone: is a three-dimensional figure that consists of a circular base and a curved laterl surface that connects the base to a cerain pointnot in the plane of th base, called the vertex. Altitude: of a cone is the perpendicular segment from the vertwx to the plane of the base. Height: of a cone is the length of the altitude Right Cone: When the altitude intersects the base of the cone at it's center.(oblique if not)

SURFACE AREA OF A RIGHT CONE 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 or S=3.14rl+3.14r(squared)

VOLUME OF A CONE The Volume, V, of a cone with radius r, height h, and base area B is V=1/3Bh or V=1/3(3.14)r(squared)h

7.6 Objectives: Define and use the formula for the surface area of a sphere Define and use the formula for the volume of a sphere Sphere: is the set of all points in space that are the same distance, r, from a given point known as the center of the sphere

VOLUME OF A SPHERE The Volume, V, of a sphere with radius r is V=4/3(3.14)r(cubed)

SURFACE AREA OF A SPHERE The surface area, S, os a sphere with radius r is S=4(3.14)r(squared)