giljos

=GIJO29= =Chapter 7 Surface Area and Volume=

7.1- Surface Area and Volume
S=2l+2w+2h [|More info on Surface Area]
 * Surface Area**- the sum of the areas of all faces of a prism.

V=lwh [|More info on Volume of Prisms]
 * Volume-** the amount of space occupied by an object

7.2- Surface Area and Volume of Prisms



 * Height**- The height of a prism is the length of an alitude
 * Altitude**- a segment that has endpoints in the planes containing the bases and is perpendicular to both planes

S=L+ 2B or S=hp+2B V=BH
 * Surface area of a right prism**
 * Volume of a Prism**

Cavalier's Principle
If two solids have equal heights and the cross sections formed by every plane parallel to the bases of both solids have equal areas, then the two solids have equal volumes

7.3- Surface Area and Volume of Pyramids



 * Pyramid**- a polyhedron consisting of a base, and three or more lateral faces
 * Base-** the polygonal face that is opposite the vertex
 * Lateral Faces-** face of a prism/pyramid that is not the base
 * Vertex of the Pyramid**- the lateral faces that share a single vertex
 * Base Edge-** the edge that each lateral face has in common with the base
 * Lateral Edge**- the intersection of two lateral faces
 * Altitude-** a segment that has endpoints in the planes containing the bases and that is perpendicular to both planes
 * Height-** the length of the altitude
 * Regular Pyramid-** a pyramid whos base is a regular polygon
 * Slant Height-** the length of an altitude of a lateral face of a regular pyramid

S=l+b or S=1/2lp+b V= 1/3Bh
 * Surface Area of a Regular Pyramid**
 * Volumes of a Pyramid**

**7.4- Surface Area and Volume of Cylinders**

 * Cylinder-** a prism with two circular bases conecting the lateral surface
 * Lateral Surface-** the area of a cylinder tha is not a base
 * Bases-** the circular translated faces
 * Altitude-** the segment that conects the bases perpendicular to both planes
 * Height- t**he length of the altitude
 * Axis-** a segment theat connects the two centerrs of the bases
 * Right Cylinder-** the axis of the cylinder must be perpendicular to both bases
 * Oblique Cylinder**- if the axis is not perpendicular to both bases

S=L+2B or S= π r h+2 π ^2 V=Bh or V=πr^2
 * Surface Area of a Right Cylinder**
 * Volume of a Right Cylinder**

7.5- Surface Area and Volume of Cones

 * Cone-** 3-D figure that has a circular base, a curved lateral surface, and a vertex
 * Base-** the circular translated faces
 * Lateral Surface-** the curved surface of a cone or cylinder
 * Vertex-** connects a single point to the base, other than in the plane of the base
 * Altitude-** perpendicular segment that connects the vertex to the plane of the base
 * Height-** the height of the altitude
 * Right Cone-** when the altitude intersects the center of the base of the cone
 * Oblique Cone-** when the altitude does not intersect the center of the base

S=L+B or S=π r l+π r^2 V=1/3Bh or V=1/3 π r^2
 * Surface Area of a Cone**
 * Volume of a Cone**

7.6 Surface Area and Volume of Spheres

 * Sphere** - The set of all points in space that are the same distance from a given point known as the center of the sphere.
 * Annulus** - The ring-shaped figure within the sphere

S=4 (3.14) r² V=4/3 (3.14)r³
 * Surface Area of a Sphere**
 * Volume of a Sphere**