haweli

=hael630 Chapter 9 Link=

[[image:cubes.jpg width="76" height="61"]]
//--here is where I// [|found] this picture.

Surface Area and Volume for a Right Rectangular Prism
++ here is a great [|website] to help you with formula. -- //scroll the a th ird of the way down to find the formulas and pictures.//

Surface Area Formula
s = 2lw + 2wh + 2lh

Volume Formula
v = lwh

Surface Area Formula
s = 6s²

Volume Formula
v =s³ [|++here is a visual] to help you with the formulas. ++ here is a [|step by step problem to help you.] Example: A righ rectangular prism thas a length of 12 width of 7 and a height of 3, what is the volume? L = 12 W = 7 H = 3 v = 12 x 7 x 3 v = 252

=**__7.2 Surface Area and Volume of Prisms__**=

~ Use Cavalieri's Principle to develop a formula for the volume of a right or oblique prism.

 * There are many different kinds of prisms such as right rectangular prism, right hexagonal prism, triangular right prism.[|here is a picture of a prism that some one made.]

Prisms
__Altitude__ - a segment that has endpoints in the planes containing the base to a line containing the bases and is perpendicular to both planes. __Height__- the length of an altitude

Surface area formula
S=L+ 2B __or__ S=hp+2B

Volume formula
V = Bh

Cavalieri's Principle
This principle was invented by Cavalieri Bonaventura[| here is his history].

If two solids have equal altitude, the sections made by planes parallel to and at the same distance from their bases are always equal, then the volume of the two solids are equal. ++here is a volume [|problem] to help you understand more. Example: If a prism has a base area of 45 and a height of 5, what is the volume? B = 45 h = 5 v = 45 x 5 v = 225

=__7.3 Surface Area and Volume of Pyramids__=

Vocab
++ here is where I [|found] this picture. __Pyramid__- A three-dimensional solid whose __base__ is a polygon and whose sides are triangles that come to a point at the top and consists of three or more __lateral faces.__ Which are triangles that both share one vertex. And that one vertex is the __vertex of the pyramid.__ Of those three lateral faces each has only one edge st with each other with the base that is called a __base edge.__ Where the two lateral faces intersect it is called a __lateral edge. Altitude__ of a pyramid is the perpendicular segment from the vertex to the plane of the base. The __height__ of a pyramids the length of its altitude. Regular pyramid is a pyramid with a base that is a regular polygon. The apex is not necessarily directly above the center of the base. The length of an altitude of a lateral face which is of a regular pyramid is called the __slant height__ of the pyramid. //add pyramids pg 445// ++ Here is a great web site to help you understand pyramids more![| regular pyramids].
 * Pyramids are named by the shape of their base

Surface Area of a Regular Pyramid.
SL + B __or__ S 1/2 lp + B

Volume of a Pyramid
V = 1/3 Bh ++ here is a volume [|problem] with the steps already there to help you Example: If a pyramid has a base area of 30 and a height of 2, what is the volume? B = 30 h = 2 v = 1/3 x 30 x 2

=**__7.4 Surface Area and Volume of Cylinders__**=

Vocab
++ Here is where I [|found] this picture __Cylinder__ - A three-dimensional geometric figure with parallel congruent bases with a __lateral surface__ connecting the circles. __Bases__ are the circular region and its translated image. __Altitude__ of a cylinder is a segment that has endpoints in the planes containing the bases and is perpendicular to both plans. The __height__ of a cylinder is the length of an altitude. The __axis__ of a cylinder is the segment joining the centers of the two bases. If the axis of a cylinder is perpendicular to the bases, then the cylinder is a __right cylinder__. If not, it is an __oblique cylinder.__ ++ Here is a helpful website with visuals of a [|right cylinder] and of a [|oblique cylinder].

Surface Area Formula
S=L + 2B __or__ S=2(pi)rh + 2(pi)r²

Volume Formula
V = Bh __or__ V (pi)r²h ++ Here is a [|problem] with the steps to help you //--it is the first one on the page.// KEY CONCEPT Here is a key concept discussed in class Q. How does doubling the height and radius of a cylinder affect the volume? A. It multiples the volume by 8 Example: If a cylinder has a radius of 3 and a height of 4 what is the volume? r = 3 h =4 v = (pi) 3² x 4 v = 113.1

=__7.5 Surface Area and Volume of Cones__=

~Define and use the formula for the volume of a cone
[|++here is a great link for help with vocab and formulas] //-- scroll down to the cone section, after the picture of the potato chips.//

Vocab
__Cone__ - is a 3D figure that consists of a circular bas and a curved __lateral surface__ that connects the base to a single point not in the plane of the base, called the __vertex.__ The __altitude__ of a cone is the perpendicular segment from the vertex to the plane of the base. The __height__ of the cone is the length of the altitude. If the altitude of a cone intersects the base of the cone a its center, then the cone is a __right cone__. If not, it is an __oblique cone.__

Surface Area and Volume of a Right Cone
L - lateral area B - base area r - radius l - slant height

Surface Area Formula
S=L+B __or__ S=(pie)rl+(pie)r²

Volume Formula
V=1/3Bh __or__ V=1/3(pie)r²h ++ here is a [|problem] that shows you how to use the volume formula. --//it is the second question.// Example: If a right cone has a Base area of 3 and a height of 14 what is the volume? B = 3 h = 4 v = 1/3 x 3 x 14 V = 14

=**__7.6 Surface Area and Volume of Spheres__**=

Vocab
__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.

Surface Area and Volume Formulas for a Sphere
r - radius

Surface Area Formula
S = 4(pie)r²

Volume Formula
V = 4/3(pie)r³ ++[|here practice your volume formula] --//scroll all the way down towards the page it is the last problem// Example: If a sphere has a radius of 12, what is the surface area? r = 12 s = 4 (pi) 12³ s = 21714.69

Here are some step by step problems
++ solve by putting numbers into calculator 1. Volume of Triangular Prism formula - 1/2lwh l= 2 w= 4 h= 6 put numbers in 1/2(2)(4)(6) solve 1/2(2)(4)(6) = 24 2. Surface area of a Triangular Prism formula - 2B + Ph B= 3 P= 6 h= 9 put numbers in 2(3) + (6)(9) solve 2(3) + (6)(9) = 60 3. Volume of pyramid formula - 1/3 bh b= 3 h=7 put numbers in 1/3(3)(7) solve 1/3(3)(7)= 7 4. Surface Area of Pyramids formula - SL + B S= 4 L= 8 B= 12 put numbers in (4)(8) + (12) solve (4)(8) + (12) = 44 5. Volume of a cylinder formula - bh b= 8 h=9 put numbers in (8)(9) solve (8)(9)= 72 6. Surface area of a cylinder formula - SL+B S= 7 L= 6 B= 2 put numbers in (7)(6)+(2) solve (7)(6)+(2) = 44 7. Volume of Cone formula - 1/3Bh B= 5 h=9 put numbers in 1/3 (5)(9) solve 1/3(5)(9) = 15 8. Surface Area of Cone formula - L+B L= 7 B= 4 put numbers in 7+ 4 solve 7+4 = 11 9. Volume of Sphere formula - 4/3(pie)r³ r= 6 put numbers in 4/3(pie)6³ solve 4/3(pie)6³ = 904.78 10. Surface Area of Sphere formula - 4(pie)r² r= 3 put numbers in 4(pie)3² solve 4(pie)3² = 113.10