3kanash

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**__//The following is a discussion of Surface Area and Volume for solid figures.//__** Informational Link to [|Prisms]
The surface area, S, and the volume, V, of a right rectangular prism with legnth, //l,// width //w,// and height //h// are S= 2 //lw// + 2 //hw +// 2 //lh// and V =//lwh.// The surface area, S, and volume, V, of a cube with side //s// are S= 6//s^2 and V=s// ^3
 * __[[image:penguin.jpg width="60" height="79" link="http://www.flickr.com/photos/thedepartment/90828664/"]]Surface Area and Volume__**

[|Link to cool games that will help you learn about the surface area and volume of objects and other vocab words that are included in this wiki.] Altitude- a segment that has endpoints in the planes containing the bases and that is perpendicular to both planes. Height- the length of an altitude. Surface area of a right prism- 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 //Example:// 1 gallon = 0.134 cubic feet and 1 gallon of water = 8.33 pounds
 * [[image:penguin.jpg width="62" height="86" link="http://www.flickr.com/photos/thedepartment/90828664/"]]Surface Area and Volume of [|Prisms]**

How many gallons of water can the aquarium hold? How much will the water weigh?

V=Bh =lwh = (465)(74)(9) = 309,690 V= 309690 ÷ 0.134 = 23,111,194.03 gallons weight = ( 23,111,194.03)(8.33) = 192,516,246.3 pounds

Pyramid- a polyhedron consisting of a base and three or more lateral faces. Base- a polygon. Lateral Faces- triangles that share a single vertex (vertex of a pyramid). Vertex of the pyramid- lateral faces of a triangle. Base edge- A lateral face that has a common edge with the base. Lateral edge- Where two lateral faces intersect. Altitude- The perpendicular segment from the vertex to the plane of the base. Height- The length of a pyramids altitude. Regular pyramid- A pyramid thats base is a regular polygon and its lateral faces are congruent isosceles triangles. Slant height- The length of an altitude of a lateral face of a regular pyramid. Surface area of a regular polygon - 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= 1/2 //lp+B.// Volume of a pyramid- The volume, V, of a pyramid with height h, and base area B is V= 1/3 Bh //Example: [|How were pyramids built?]// The pyramid shown has a base edge of 853 feet and a height of the pyramid is 591 feet. Using the Volume of a Pyramid formula, find the weight of the solid pyramid.
 * [[image:penguin.jpg width="56" height="86" link="http://www.flickr.com/photos/thedepartment/90828664/"]]Surface Area and the Volume of Pyramids**

V= 1/3 bh = 1/3 (853^2)(591) = 143338973 cubic feet [|Cylinder-] A solid that consists of a circular region and its translated image on a parallel plane, that has a lateral surface connecting the circles. Lateral Surface- The curved surface of a cylinder. Bases- The faces formed by the circular region and its translated image. Altitude- A segment that has endpoints in the planes containing the bases and is perpendicular to both planes Height- The length of n altitude. Axis- A segment joining the centers of two bases. Right cylinder- If the axis of a cylinder is perpendicular to the bases. Oblique cylinder- If the axis of a cylinder is not perpendicular to the bases. 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 π r h + 2 π r ^ 2. The Volume, V, of a cylinder with a radius r, base B, and height h is V=Bh or V= π r ^2 h [|Cone-] A three dimensional figure that consists of a circular base and a curved lateral surface. Base- A circular and flat area on the bottom of the cone. Lateral Surface- The curved area that surrounds the cones base. Vertex- Where the lateral surface comes together at a single point of a cone, it is not the plane of the base. Altitude- The perpendicular segment from the vertex to the plane of the base. Height- The length of the altitude. [|Right cone-] where the altitude intersects at the center of the base. Obilque cone- where the altitude doesn't intersect at the center of the base. Slant height- the length of an altitude of a lateral face. 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= π r l + π r ^2. The Volume, V, of a with radius r, height h, and base area B is V= 1/3 Bh or V= 1/3 π r^2 h. [|Sphere-] the set of all points in space that are the same distance from the center of the sphere. The volume, V, of a sphere with radius r, is V= 4/3 π r^2s The surface area, S, of a sphere with radius r is S= 4π r^2 [|Annulus-] The region between two circles in a plane that has the same center point but different radius.
 * [[image:penguin.jpg width="66" height="80" link="http://www.flickr.com/photos/thedepartment/90828664/"]]Surface Area and Volume of Cylinders**
 * [[image:penguin.jpg width="60" height="79" link="http://www.flickr.com/photos/thedepartment/90828664/"]]Surface Area and Volume of Cones**
 * [[image:penguin.jpg width="60" height="79" link="http://www.flickr.com/photos/thedepartment/90828664/"]]Surface Are and Volume of Spheres**