clader

clde317 link to chapter 9

=Chapter 7=

Section 1
Surface Area and Volume Formulas Key Symbols: S= Surface area, V= volume, L= length, H= hight, W= width, s- side of a square(cube), B= Base, P= Perimeter
 * S=2Lw+2Wh+2Lh, V= LW
 * Cube= 6 s², V=s ³.

[|Flickr.com Cube] Try this A box company wants to choose the box with the most volume, but as little surface area as posible. Box A's dimentions- 4×8×10 and box B's dimentions are-2×10×8. Box A's surface are= 184 units²= 2(80)(5)+2(4)(5)+2(4)(8) Box B's surface are 232 units²=2(10)(8)+2(2)(8)+2(2)(10) Box A has the least surface area.

Here's a link that will help you understand area of a cube.[|Calculate surface area]. Try the games.

Section 2
Surface area of a right prism Volume of a Prism Cavaliere's Principle //Vocab Words//: [|Flickr.com Right Prism]
 * S= L+2B
 * V=BH
 * 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.
 * Altitude**- is a segment that has endpoints in the planes containing the bases and that is perpendicular to both planes
 * Height**- is the length of the //altitude//

Section 3
[|Regular Pyramid- Flickr.com] Surface area of a Regular Pyramid Volume of a Pyramid
 * S= L=B or S= 1/2 LP=B
 * V=1/3 BH
 * Pyramid**- Is a polyhedron consisting of a base, and three or more lateral faces
 * Lateral Faces**- triangles that share a single vertex called the vertex of the pyramid
 * Base**- a polygon
 * Vertex of the Pyramid-** the topmost point of the pyramid
 * Altitude-** is the perpendicular segment from the vertex of the plane of the base
 * Hight**- length of the altitude
 * Regular Pyramid**- is a pyramid whose base is a refular polygon and whose lateral faves are congruent isosceles triangles

Section 4- Surface area and Volume of Cylinders
Surface area of a Right Cylinder Volume of a Culinder Vocab Words-
 * S=L+2B
 * V= Bh or V=3.14 r² h
 * Cylinder**- a solid that consists of a circular region and its translated image on a parallel plane with a lateral face connecting the circles
 * Lateral face**- the side of the cylinder
 * Bases**- the faces formed by the circular region and its translated image are the bases
 * Altitude**- is a segment that has endpoints in the planes containing the bases and is perpendicular to both planes
 * Axis**- the segment joining the centers of the two bases
 * Right Cylinder-**if the axis of the cylinder are perpendicular to the bases
 * Oblique Cylinder-** if the axis of the cylinder are not perpendicular to the bases

Activity: Try this

A car tire is a right cylinder with a diamiter of 20 inches and a thicknes of 10 inches. Estimate the surface area.

The radius of the tire ids half the diameter, or 10 inches. Use the formula below for the surface of a right Cylinder.(assume the wheel is part of the tire in this problem and is solid) S 2-3.14rh+2-3.14r². S2-3.14(10)(10)+ 2-3.14(10)² is about1256.64 inches²

Section 5- Surface area and Volume of Cones

 * Cone**- is a three-dimensional figure that consists of a circular Base and a curved lateral surface that connects the base t a single pont not in the plane of the base, called a vertex
 * Vertex-** topmost point in the cone
 * Altitude**- is the perpendicular segment from the vertex to the plane of the base
 * Hight**- lenth of altitude
 * Rigth Cone**- the altitude of the cone intersects the base of the cone at ist center
 * Oblique Cone**- doesnt meet in center of cone

Surface area of cone > Volume [|Cone from Flickr]
 * S=L+B
 * V=1/3Bh

Section 6- Surface area and Volume of Spheres
Volume of a sphere > Surface area of a sphere
 * Sphere-** is the set of all points in space that are the same distance from a given point known as the center of the sphere.
 * V=4/3×3.14r³
 * S=4×3.14r²

[|Skeleton of a sphere-Flickr.com]

Something we did as a clas was discus how to find out how much a shpere would take up inside a cube. We found out that a cube and a sphere that had the same volume had different surface areas. The square had 600units³ and the sphere had around 483.6units³ and found out the sphere would fit insid only taking up only 80% of the cube.

[|Sphere- Flickr.com]

This web site has a couple of games and has all of the volume formulas and surface-area formulas you will need. Try it. [|Volume and Surface-Area]Scroll down about half way to find formulas.