mecemi

MEEM115 ch 9 link

7.1: The surface area, S, and volume, V of a right rectangular prism with length //L,// width w, and height h are //S= 2lw+2wh+2lh// and V//= l//wh//.// click [|here] to see examples to this chpt. [|surface area]
 * Surface area and Volume Formulas:**

7.2 An altitude of a prism is a segment that has endpoints in the planes containing the bases and that is perpendicular to both planes. [|right prism] The surface area, 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 [|CLICK] TO SEE SA of a right prism- scroll down a ways on the page! click [|here] for a sweet game to play! Use-S=L+2B S=3+2(4) S=3+8 S=12
 * Surface area of a right Prism:**
 * Volume of a Prism:** V, of a prism with height h and base area B is V= Bh
 * Example:** Lateral area of a right prism is 3 and the base is 4.

7.3 S, of a regular pyramid with lateral area l, base B, perimeter of the base p, and slant height L is S=L+B or S= 1/2lp+B Slant Height: Altitude length of lateral faces If the lateral area is 5, perimeter of the base is 2 and base area is 10 S=1/2(5)(2)+10 S=5+10 S=15
 * Surface Area of a regular Pyramid:**
 * Pyramid**: A solid having a polygonal base, and triangular sides that meet in a point
 * Base**: The line or surface forming the part of a figure that is most nearly horizontal or which it is supposed to stand
 * Lateral faces**: The face or surface of a solid on its sides. That is, any face or surface that is not a base
 * Vertex of the pyramid:** The fixed point at the intersectino of all the faces of the pyramid
 * Base edge**: Common edges within lateral faces
 * Lateral edge**: where two lateral faces meet
 * Altitude:** The perpendicular distance from the vertex of a figure to the side oppsite the vertex or the line through the vertex of a figure perpendicular to the base
 * Height:** Extent or distance upward to a fixed point
 * Regular Pyramid:** At its base
 * Example:**

click [|here] for examples

V, of a pyramid with height h and base area B is V=1/3 bh.
 * Volume of a pyramid:**

7.4 [|cylinder] click [|here]
 * Surface area of a right cylinder:** Of a right cylinder with lateral area, l base area B, radius r, and height h is S=:+2B or S=2 3.14h+2 3.14r2
 * Volume of a Cylinder:** of a cylinder with radius r, height h, and base areaB is V=bh or V=3.14h
 * Lateral surface:** The face or surface of a solid on its sides. That is, any face or surface that is not a base
 * Bases:** Bottem and top circular part of a cylinder
 * Altitude:** The line through the vertex of a figure perpendicular to the base
 * Height:** Distance upward from a given level to a fixed point
 * Axis**: A line about which a 3-dimensional body
 * Right cylinder:** A cylinder which has bases aligned one directly above the other

7.5 Volume of a cone: V= 1/3. 3.14 R2h** click [|here] for examplesLateral surface: Connects the circles of a cylinder.
 * Surface area of a right cone : SA= 3.14RS= 3.14R ^R2+H2

S=L+B or S=(Pi)rx+(Pi)r^2
 * Base:** circular base
 * Lateral surface:** Curved lateral surface
 * Altitude:** The perpendicular segmentfrom the vertex to the plane of the base.
 * Height**: The length of the altitude.
 * Right cone:** If the altitude intersects the center of the cone.
 * Oblique cone:** If the altitude does not intersect the center of the cone.
 * Surface area of a right cone:**

(Pi)= 3.14

r= radius

x= slant height

cone - is a 3 dimensional figure that has a circular base with a curved lateral surface that connects the base that is not in the sphere - a set of all the points in space the same distance from a given point in the center of the sphere Volume of a sphere: V= 4/3 3.14r3 V= 4/3πr³ The surface area, S, of a sphere with radius r is S= 4πr²
 * 7.6**

Example:V= 4/3πr³ V= 4/3π (5) ³= 4/3π125 = 4/3 * 125π = 166.66666666625in³ π = about 523.59877559699in³

Volume of a sphere: V= 4/3 3.14r3

click [|here] for a example of a volume of a sphere

> V=1/3 3.14r2 h
 * 1) **surface area of a triangle-** if its height is 7 base area 36 base perimeter is 23 so S= hp+2B so S=(7)(23)+2(36) so you just put that into the your calculater and it gives you the surface area.
 * 2) volume of a triangle- V=Bh so V=(36)(7)
 * 3) volume of a pyramid-what is the volume of a pyramid if thel is 6 and the area of the base=9 and the perimeter of the base=12 and the height was 8. so V=1/3bh V=1/3(9)(8)
 * 4) surface area of a pyramid- S=1/2 lp+B S=1/2(6)(12)+9
 * 5) volume of a cylinder- what is the volume of a cylinder if its height is 7 and its radius is 4? V=pie r^2(7) V=pie(4)^2(7)
 * 6) surface area of a cylinder- SA=2pie rh+2pie r^2 so SA= 2pie(4)(7)+2pie(4)^2 [[image:http://argyll.epsb.ca/jreed/math9/strand3/images/cylinder_net_sml.gif width="149" height="125"]]
 * 7) Volume of cone: V= 1/3 Bh
 * 1) volume of a cone- what is the volume of a cone if it has a radius of 4 a height of 8 and a l of 12. V=1/3 pie r^2h so V=1/3pie(4)^2x(8)
 * 2) surface area of a cone- S= pie rl +pie r^2 so S=pie(4)(12)+pie(4)^2 [[image:http://argyll.epsb.ca/jreed/math9/strand3/images/sphere_volume.gif width="120" height="118"]][[image:http://argyll.epsb.ca/jreed/math9/strand3/images/sphere.gif width="121" height="121" align="center"]]
 * 3) volume of a sphere- what is the volume if the radius it 6. so V=4/3pie r^3 then V=4/3pie(6)^3
 * 4) surface area of a sphere- S=4pie r^2 so plung in r S=4pie
 * 1) surface area of a sphere- S=4pie r^2 so plung in r S=4pie