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josh hoffmans chapter 9 wiki

//7.1 Surface Area and Volume//


[|Surface area formulas for right rectangular prisms] S=2//lw + 2wh + 2lh// For a cube the formula is S=6s²

__Volume formulas for right rectangular prisms__ V=//lwh// For a cube the formula is V=s³

__Ratio of surface area to volume__ The surface area to volume ratio is important in helping to find the maximum and minimum volume. It is helpful in maximizing your volume while still having a low production cost. It is also important to help minimize your volume for storage and other things where you have a restricted amount of space.

//7.2 Surface Area and Volume of Prisms//
__DEFINITION OF **Altitude** of a prism__ A segment that has endpoints in planes that are containing both of the bases and is perpendicular to both planes.

__DEFINITION OF **Height** of a Prism__ The height of a prism is the length of the altitude.

__Surface area formulas for a right prism__ S-surface area L-lateral area B-base area P-perimeter H-height

S=L + 2B or S=HP + 2B

__Volume formula for a prism__ V=BH

[|Cavalieri's Principle] If two solids have a equal height and the cross section formed by all of the parallel planes to the bases have the same area, then their volume is the same also.

//[|7.3 Surface Area and Volume of Pyramids]//
__ Definition of **pyramid**__ A polyhedron in which all but one of the polygonal faces intersect at a single point known as the vertex of the pyramid

__Definition of **base**__ The polygonal face that is opposite the vertex

__Definition of **lateral faces**__ Faces of the pyramid

__Definition of **regular pyramid**__ A pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles

__Definition of **slant height**__ In a regular pyramid, the length of an altitude of a lateral face

__Surface area of a regular pyramid__ S-surface area L-lateral area B-base area p-perimeter of the base //l// - slant height

S= L + B or S= .5//l//p + B

__Volume of a pyramid__ V-volume h-height B-base

V=1/3Bh

//[|7.4 Surface Area and Volume of Cylinders]//
__Definition of **Cylinder**__ A solid that consists of a circular region and its translated image in a parallel plane with a lateral surface connecting the circles

__Definition of **lateral surface**__ The curved surface of a cylinder or cone

__Definition of **right cylinder**__ A cylinder whose axis perpendicular to the bases

__Definition of **oblique cylinder**__ A cylinder that is not a right cylinder

__Surface area of a right cylinder__ S-surface area L-lateral area B-base area r-radius h-height

S = L + 2B or S = 2(3.14)rh + 2(3.14)r²

//[|7.5 Surface Area and Volume of Cones]//
__Definition of **cone**__ A 3-D figure that consists of a circular base and a curved lateral surface that connects the base to a single point not in the plane of the base, called the vertex

__Definition of **right cone**__ A cone in which the altitude intersects the base at its center point

__Definition of **oblique cone**__ Any other cone that is different than a right cone

__Surface area of a right cone__ S-surface area L-lateral area B-base area r-radius //l//-slant height

S = L + B or S = (3.14)r//l// + (3.14)r²

__Volume of a cone__ V-volume r-radius h-height B-base area

V = 1/3 Bh

//[|7.6 Surface Area and Volume of Spheres]//


Definition of **sphere** The set of points in space that are equidistant from a given point known as the center of the sphere

__Volume of a sphere__ V-volume r-radius V = 4/3(3.14)r³

__Surface area of a sphere__ S-surface area r-radius

S = 4(3.14)r²

1. Volume of a triangular prism 2. Surface area of a triangular prism 3. Volume of a pyramid 4. surface area of a pyramid 5.volume of a cylinder 6. surface area of a cylinder 7. volume of a cone 8. surface area of a cone 9. volume of a sphere 10. surface area of a sphere