3piaand

[[image:cube3piaand.JPG]]
__**The surface are, S, and volume, V, of a right rectangular prism with length L, width W, and height H, are:** S = 2LW + 2WH +2LWH V = LWH

S = 6s² V = s³__
 * The Surface area and volume of a cube:**

__**Example Problem** A cereal company is choosing between two box designs with the demensions: Box A= 8in(h) x 4in(w) x 5in(l), Box B = 10in(h) x 8in(l) x 2in(w). which box has greater surface area and requires more meterial for the same price?

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.
 * Solution**

Box B has the greater surface area.
 * Answere**



[|Section 2 - Surface Are and Volume os Prisms] Deffinitions to know__ Altitude- Altitude of a prism is a segment that has endpoints in the panes containing the bases and that is perpendicular to both planes. Height- The leangth of an altitude.

__**Surface Area of Right Prism** -__ The surface area,S, of a right prism with a lateral area,L, base area,B, permieter,P, snd height,H, is S=L+2B or S=HP+2B

__**Cavalieris 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 planes have equal volumes.

__**Volume of a Prism** -__ The volume,V, of a prism with height,H, and base,B, is V=BH



[|Section 3 - Surface Area and Volume of a Pyromid]

__Deffinitions to know__ Pyromid - polyhedron consisting of a base Base - polygon with three or more lateral faces Lateral Faces - triangles that have the same single vertex Vertex of the Pyromid - triangles that share a vertex Base edge - each lateral face has a common edge Lateral edge - intersection of two lateral edges Regular Pyromid - pyromid that has a base is a regular polugon Slant Height - leangth of altitude

__Surface Area of a regular Pyromid__ The surface area,S, of a regular pyromid with lateral area,L, base area,B, perimeter of base,P, and a slant,l, is S=L+B or S=1/2lP+B __**Example:** Problem:__ The roof of a gzebo is a regular octogonal pyromid with a base ede of 4 feet and a slant height of 6 feet. find the area of the roof. if roofing meterials costs $3.50 per square foot, find the cost of covering the roof with the meterial. Solution: The area of the roof is the lateral area of the pyromid. L=1/2lP=1/2(6)(8x4) = 96square feet. 96 square feet x $3.50 =$336.00

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



[|Section 4 - Surface Area and Volume of a Cylinder]

Deffinitions to know__ Cylinder - A solid that consists of a circular region (pillar) Right Cyinder - If the axis of the cylinder is perpendicular to the base. Oblique Cylinder - If the axis of the cylinder is not perpendicular to the base.

__**Surface Area of a Right Cylinder**__ The surface area,S, of a rigt clinder with lateral area,L, base area,B, radious,R, and height,H, is S=L+2B or S=pieRH + 2pieR².

__**Volume of a Cylinder**__ The volume,V, of a cylinder with radious,R, height,H, and base area,B,is V=BH or V=pie²H



[|Section 5 - Surface Area and Volume of Cones] __Deffinitions to know__ Cone - A three-demensional 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 Cone - Anything Besides a right cone

__**Surface Area of a Right Cone**__ 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

__**Volume of a Cone**__ The volume,V, of a cone with a radius,R, height,H,and base area,B, is V = 1/3BH [|Section 6 - Surface Area and Volume of Spheres] __Deffinitions to know__ Sphere - Is the set of all points in a space that are the same distance. Annulus - Ring shaped figure

The volume,V, of a sphere with radius,R, is V=4/3pirR³
 * __Volume of a Sphere__**