sprshe

spsh516 chapter 9 wiki
=__Chapter 7__=

Lesson 7.1 =Objectives=
 * 1) Explore ratios of surface area to volume.
 * 2) Develope the concepts of maximizing volume and minimizing surface area.

//Surface Area and Volume Formulas// The surface area, //S//, and the volume, //V//, of a right rectangular prism with length //l//, and width //w//, and height //h// are: //S//=2//lw//+2//wh//+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=s³//

Vocab

__Lesson 7.2__
=__Objectives__=
 * 1) Define and use a formula for finding the surface area of a right prism.
 * 2) Define and use a formula for finding the volume of a right prism.
 * 3) Use Cavalieri's Principle to develope a formula for the volume of a right or oblique prism.

If the sides of the base are s[1], s[2], and s[3] and the height is //h,//then the lateral area is given by the following formula: //L=s//[1]//h+s//[2]//h+s//[3]//h=h//(//s//[1]+//s//[2]+//s//[3])

//Surface Area of a Right Prism// The surface are, //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//

//Cavalieri's 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 then the two solids have equal volumes.

//Volume of a Prism// The volume, //V//, of a prism wiht height //h// and base area //B// is: //V=Bh//

Vocab

__Lesson 7.3__
= = =__Objectives__=
 * 1) Define and use a formula for the surface area of a regular pyramid.
 * 2) Define and use a formula for the volume of a pyramid.

//Surface Area of a Regular Pyramid// The surface area, //S//, of a regular pyramid with lateral area //L//, base area //B//, perimeter of the base //p//, and the slant height //l// is: //S//=½//lp+B// //S=L+B// or [|] [|//TEST YOUR SKILLS!(52)//]

//Volume of a Pyramid// The volume//, V,// of a pyramid with height //h// and base area //B// is: //V=//¹/³//Bh// [|//Test Your Skills(52,7.3V)//]

Vocab

__Lesson 7.4__
=__Objectives__=
 * 1) Define and use a formula for the surface area of a right cylinder.
 * 2) Define and use a formula for the volume of a cylinder.

//Surface Area of a Right Cylinder// 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**rh+2**π**r² [|Test Your Skills!(52,7.4)]

//Volume of a Cylinder// The volume, //V//, of a cylinder with radius //r//, height //h//, and base area //B// is: //V=Bh or V=**π**r²h// [|Test Your Skills(52V)]



Vocab

__Lesson 7.5__
=__Objectives__=
 * 1) Define and use the formula for the surface area of a cone.
 * 2) Define and use the formula for the volume of a cone.

//The Surface Area of a Right Cone// The surface area, //S//, of a right cone with lateral area //L//, vase of area //B//, radius //r//, and slant height //l// is: //S=L+B or S=**π**rl+**π**r² [|Test Your Skills!(52,7.5)]//



//Volume of a Cone// The volume, //V//, of a cone with radius //r//, height //h//, and base area //B// is: //V=¹/3Bh or V=¹/3**π**r²h// [|Test Your Skills(52,7.5V)]

Vocab

__Lesson 7.6__
=Objectives=
 * 1) Define and use the formula for the surface area of a sphere.
 * 2) Define and use the formula for the volume of a sphere.

//Surface Area of a Sphere// The surface area, //S//, of a sphere with radius //r// is: //S=//4**π**//r² [|Test Your Skills(52,7.6)]

Volume of a Sphere// The volume//, V,// of a sphere with radius //r// is: //V=//4/3**π**r³ [|Test Your Skills!(52,7.6V)]

Vocab