3flukar

=Here's some things about surface area & volume. Link to a cool website on [|surface area &][| volume]= _

=__Surface Area & Volume Walkthrough__= = = =Formulas= __Rectangular Prism__ Surface area= 2lw+2lh Volume= lwh

__Cube__ SA= 6s² V= s³

=Example= You are an executive for a packing company and you need to find a way to make a box that has the smallest possibe surface area for the largest possible volume. This saves material. And Money.

=__SA & V of Prisms__= [|More info on Prisms]

Volume=Length x Width x Height essentially, L x W = Base so L x W x H is the same as saying B x H The altitude is a vertical segment connecting the two bases. The height is the length of the altitude. Surface Aea = Length + 2 x Base or Height x Perimeter + 2B
 * __Formulas for a Right Prism__**

=**Cavalieri's Pri**nciple= If two solid figures have the same height and the cross sections of both figures are parallel to their bases, then the figures have the same volume

Take this example, you have two stacks of cards, both have the same number of cards. If you tip one a little, the volume hasnt changed. =__Pyramids__= A pyramid is a polyhedron with a base and three or more faces that share a vertex.

A regular pyramid is a pyramid with a regular polygon for the base and its lateral faces are congruent isosceles triangles.

The segment that intersects the vertex of the pyamid and is perpendicular to the base is called the altitude.

The length of an altitude of a lateral face of a right pyramid is the slant height of the pyramid.

__SA for a regular pyramid__ The formula for the SA of a regular pyramid is SA = LA + B LA is the lateral area.

__Volume of a Regular Pyramid__ V = 1/3 x B x H

=__SA & V of Cylinders__= A cylinder is a solid that is composed of a circle and its translated figure onto a parallel plane with a lateral surface connecting the circles.

The cicles of the cylinder form the bases.

The altitude of a cylinder is a segment that connects both bases with endpoints in both of their planes. The altitude is completely vertical. The height is the length of the altitude.

The axis is a segment that joins the middle of the two bases. (it does not necesarily have to stay completely vertical) If the axis of a cylinder is perpendiclar to its bases the the cylinder is a right cylinder. If it it is not, then it is an oblique cylinder.

__Formulas__ (Surface Area) SA = L + 2 x B or S = 2 x pi x r x H + 2 x pi x r²

(Volume) V = B x H or V = pi x r² x H

= = =SA & V of cones=

A cone is a 3D figure that has a circular base with a curved lateral face that connects the base to a single vertex out of the plane that the base is in.

The altitude is the segment that connects the point of the cone to the base.

The height is the altitude's length.

__Surface Area of a Right Cone__ Surface area = the lateral area + the base area SA = L + B

__Volume of a Cone__ V = 1/3 x B x H

=__SA & V of Spheres__= A sphere is a set of points in space that are the same distance from a single midpiont.

__Formula for Volume__ V = 4/3 x πr²

__Formula for SA__ S = 4πr²