sivama

= = siam620 ch9link =__7.1 surface area and volume__= Objectives: ~ Explore ratios of surface area to volume. ~ Develope the conceps of maximizing volume and minimizing surface area. The surface area and volume of a rectangular prism** S= 2lw + 2wh + 2lh V= lwh
 * Surface Area and volume formulas

S= 6s^2 V= S Rectangular prism
 * The surface area and volume for a cube**


 * lenght || surface area || volume || surface area/volume || ratio ||
 * 1 || 6u^2 || 1u^3 || 6/1 || 6 ||
 * 2 || 10u^2 || 2u^3 || 10/2 || 5 ||
 * 3 || 14u^2 || 3u^3 || 14/3 || 4.6 ||

=This cube is 6X6= =Find the surface area and volume::= =Surface Area: 6X6^2= 216u^2= =Volume:6X6^3= 1296u^3=
 * EXAMPLE!!!**


 * Sides || Surface Area || Volume || Surface Area/ Volume || Ratio ||
 * 1 || 6u^2 || 1u^3 || 6/1 || 6:1 ||
 * 2 || 24u^2 || 8u^3 || 24/8 || 3:1 ||
 * 3 || 54u^2 || 27u^3 || 54/27 || 2:1 ||
 * n || 6n^2 || n^3 || 6n^2/n^3 ||  ||

=__7.2 Surface Area and Volume of Prisms__=

Objectives: ~ Define and use a formula for finding the surface area of a right prism. ~ Define and se a formula for finding the volume of a right prism. ~ Use Cavalieri's Principle to develope a formula for the volume of a right or oblique prism.

S= L+2B or S= hp+2B If two solides have the same heights and cross sections formed by all planes of both solids have the same area, that means they have the same area too. V=Bh
 * Altitude:** A segment that has endpoints in the planes containing the bases and is perpendicular to both planes.
 * Height:** The lenght of the altitude.
 * Surface Area of a right prism:**
 * What is Cavalieri's Principle??**
 * Volume Of A Prism:**



=__7.3 Surface Area and Volume of Pyramids Objctives__=
 * ~** Define and use a formula for the surface area of a regular pyramid.

S= L+B or S= 1/2lp+B V= 1/3Bh
 * ~** Define and use a formula for the volume of a pyramid.
 * Surface Area of a regular pyramid:**
 * Volumes of a Pyramid**
 * Example: use the volume and surface area formulas to find the volume and surface area to the triangular prism above.**

=__7.4 Surface Area and Volume of Cylinders.__= ~ Define and use the formula for the surface area of a rigt cylinder ~ Define and use a formula for the volume of a cylinder. S= L+B or S=2(pi)rh+2(pi)r^2
 * Objectives:**
 * Cylinder:** is a solid that consists of a circular region.
 * Surface Area of a Right Cylinder.**



=__7.5 Surface Area and Volume of Cones__= S= L+B or S= (pi)rl+ (pi)r^2 V=1/3Bh or V=1/3(pi)r^2h =Example: The length is 15 and the radius is 7 find the surface area and volume.= Surface area: (pi)7X15+(pi)7^2=1803.27 Volume: 1/3(pi)7^2X15=796.69
 * Cone: is a three-dimensional figure that consists of a circular base.**
 * Surface Area of a Right Cone**
 * Volume of a Cone**



=__7.6 Surface Area and Volume of Spheres__= Objectives: ~ Define and use the formula for the surface area of a sphere. ~ Define and use the formula for the volume of a sphere. V=4/3(pi)r^3
 * Sphere:** Is the set of all points in space that are the same distance,r, from a given point known as the center of the sphere.
 * Volume of a sphere:**

Example: Find the volume of this sphere. the radius is 14. S=4(pi)r^2
 * Surface Area of a Sphere:**

[|math games]
 * //Here i found some math games and when you go to this link click on any of the bulletines there and you will find ways to help you with surface area and volume. Click on Geometry Facts and Calculations. Then proceed to whatever you need help on.//**