3petbra

We will learn about SA and V (Surface Area) and (Volume) for solid figures.
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S = Surface Area V = Volume L = Length W = Width H = Height s = Side
 * __Surface Area and Volume Formulas__**

S = 2LW + 2WH + 2LH V = LWH
 * __Surface Area and Volume of a Right Rectangular Prism__**

S = 6s² V = s³
 * __Surface Area and Volume of a Cube__**

A cereal company is choosing between two designs for a box with dimensions shown below. Which design has the greater surface area and requires more material for the same volume.
 * __Example__**

__Box A__ Length - 5 in. Width - 4 in. Height - 8 in. __Box B__ Length - 8 in. Width - 2 in. Height - 10 in. Both boxes have a volume of 160 cubic inches. The surface area of box A is 2(8)(5) + 2(4)(8) = 184 square inches. The surface area of box B is 2(10)(8) + 2(2)(8) + 2(2)(10) = 232 square inches. So, Box B has the greater surface area. Surface Area and Volume of Prisms
 * Solution**

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
 * Definitions**

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**

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.
 * Cavalieri's Principle**

The volume, V, of a prism with height //h// and bases area B is V = B//h//
 * Volume of a Prism**

[|Surface Area and Volume of Pyramids] Pyramid - a polyedron consisting of a base Base - a polygon and three or more lateral faces Lateral Faces - triangles that have the same single vertex Vertex of the Pyramid - Single vertex of the pyramid Base Edge - Each lateral face has one common edge with the base Lateral Edge - The intersection of two lateral faces Regular Pyramid - a pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles. Slant Height - The length of an altitude of a lateral face of a regular pyramid.
 * Definitions**

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
 * Surface Area of a Regular Pyramid**

The roof of a gazebo is a regular octagonal pyramid with a base edge of 5 feet and a slant height of 7 feet. Find the area of the roof. If roofing material costs $3.00 per square foot, find the cost of covering the roof with this material.
 * Example** -

The area of the roof is the lateral area of the pyramid L = ½//lp =// ½(7)(10x5) = 175 square feet 175 square feet x $3.00 per square foot = $525.00
 * Solution** -

The volume, V, of a pyramid with height //h// and base area B is V = 1/3B//h//
 * Volume of a Pyramid**

[|Surface Area and Volume of Cylinders] Cylinder - a solid that consists of a circular region and its translated image on a parallel plane Axis - the segment joining the centers of the two bases Right cylinder - the axis of a cylinder is perpendicular to the bases. Oblique cylinder - if the axis of a cylinder is not perpendicular to the bases.
 * Definitions** -

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 = 2π//rh +// 2π².
 * Surface Area of a Right Cylinder**

The volume, V, of a cylinder with radius r, height h, and base area B is V = B//h// or V = π//r//²//h//
 * Volume of a Cylinder**

[|Surface Area and Volume of Cones] Cone - A three-dimensional figure that consists of a circular base and a curved lateral face that connects at a single point Right Cone - The altitude of the cone intersects the base at its center Oblique - Anything besides a right cone
 * Definitions**

The surface area, S, of a right cone with a lateral area,L, base of area, B,radius,R, and a slant height, L, is S = L + B
 * Surface Area of a Right Cone**

The volume, V, of a cone with radius //r//, height //h//, and base area B is V = 1/3B//h//
 * Volume of a Cone**

[|Surface Area and Volume of Spheres] Definitions -** Sphere - the set of all points in space that are the same distance,//r,// from a given point known as the center of the sphere. Annulus - the ring - shaped figure in the cylinder
 * [[image:q.jpg link="http://www.flickr.com/photos/yhancik/557151275/sizes/s/"]]

V = 4/3π//r³.//
 * Volume of a Sphere -** Volume, V, of a sphere with radius //r// is

S = 4π//r²//
 * Surface Area of a Sphere -** The surface, area, S, of a sphere with raidus //r// is