kenhar

Keha517 Chapter 9


 * 7.1**

=__Surface area and volume__= The **surface area** if an object s the total area of all exposed surfaces of the object.

the **volume** of a solid object is the number of nonoverlapping unit cubes that will exacty fill the interior of the figure.


 * surface area & volume:Ractangular prism**

S=L*H*2 + W*H*2 + 2*L*H

V=l*w*h SA=6*S*2
 * Volume:**
 * L=length
 * W=width
 * H=height
 * S= Surface area
 * V=volume
 * Surface area & Volume:Cube**

V=S*3
 * Volume:**
 * S=with of sides
 * V=volume
 * SA=surface area

= =

__Rectangular Prism:__
each of these can be considered a rectangular prism.

__**Cube:**__




 * 7.2**

=__Surface area and volume of a prisms__=

the definition and formula for right prisms volume and surface area. we willl also use cavalieris principle to develope a formula to find the surface area and volume of a oblique prism**.
 * what are you going to learn??**

__SURFACE AREA:__

the formula for surface area ( SA ) of a right prism.** SA=L(length) + 2*B(base) or SA= H (height) * P (perimeter) + 2 * B (base)


 * the formula for surface area ( SA ) of a obliqe prim.

__VOLUME:__

the volume ( V ) formula for a right prism.**

V= B (base) * H (hieght)


 * __EXAMPLES:__**


 * __Common questions:__

Q:How can you tell what is an obliqe prism & what is a right prism??

A:** A right prism is when the hight is 90 degrees to the base of the prism, and has no slant to it. An obliqe prism is where the there can be two heights to the prism on is called the slant height and the other is the altitude (another word for height), this is because the prism is at a slant


 * 7.3**

=__Surface area and volume of pyramids__=

What will you be learning??

 * different kinds of pyramids
 * the formula to find the volume of a pyramid
 * the formula to find the surface area of a pyramid
 * how to draw a net to a pyramid.


 * KINDS OF PYRAMIDS:**
 * Triangular pyramid
 * Rectangular pyramid
 * Pentagonal pyramid
 * Hexagonal pyramid

SA= L +B
 * Surface Area:**
 * SA= surface area
 * B=base
 * L= slant height

V= 1/3 B * H
 * Volume:**
 * V= volume
 * B= base
 * H= height

EXAMPLES:

=**7.4**=

**Objectives**
-Define and use the formula for the surface area of a right cylinder. -Define and use the formula for the volume of a cylinder.
 * Cylinder - A solid that consists of a circular region and its translated image on a parallel plane.
 * Lateral Surface - Connects the circles.
 * Bases - Faces formed by the circular region and its translated images.
 * Altitude - A segment that has endpointsin the planes containing the bases and is perpendicular to both planes.
 * Height - Cylinder is the length of an altitude.
 * Axis - A cylinder is the segment joining the centers of the two bases.
 * Right cylinder - If the axis of a cylinder is perpendicular to the base.
 * Oblique cylinder - If its not perpendicular

EXAMPLES:

=__Surface Area and Volume of Sphere__=
 * 7.6**

__Objectives:__ Define and use the formula for the surface area of a sphere. Define and use the formula for the volume of a sphere.

s=surface area pi=pi or 3.14 v=volume r=radius
 * Sphere- The set of points in space that are equidistant from a given point know as the center of the sphere.
 * Annulus- The region between twho circles in a plane that have the same center but different radii.
 * Surface Area and Volume Formulas for a Sphere**:

S = 4(pi)r²
 * Surface Area Formula:**

V = 4/3(pi)r³
 * Volume Formula:**

EMAMPLES:


 * TRIANGULAR PRISM**

__1.volume__ V = l x w x h Example: = 12 x 7 x 10 = 840 units³

__2.surface area__ SA = 2lh + 2lw + 2wh = 2x7x10 + 2x7x4 + 2x4x10 = 140 + 56 + 80 = 276units³


 * PYRAMID**

__3.volume__ V = 1/3BH = 1/3 X 39 X 17 = 12.999 X 17 = 220.9996 units

__4.surface area__ A pyramid has a base dimension of 6 X 7 feet and has a slant height of 8 feet. Find the surface area: S=1/2(l)(p)+B S=1/2(8)(26)+(42) S=1/2(208)+(42) S=104+42 S=146 feet cubed


 * CYLINDER**

__5.volume__ A pop can has a radius of 3 inches and a height of 7 inches. Find the volume: V=(Pi)r^2h V=(Pi)3^2(7) V=(Pi)9(7) V=(Pi)63 V=197.82 inches cubed

__6.surface area__ SA=2πrh+2πr^2 if the radius is 10 and the height is 5 SA=2π(10)(5)+2π100 = 300π


 * CONE**

__7.volume__ V=1/3Bh if the base is 30π and the height is 4 V=1/3(30π)(4) = 40π

__8.surface area__ SA=πrl+πr^2 if the radius is 4 and the slant height is 2 SA=π(4)(2) + π(16) = 24π


 * SPHERE**

__9.volume__ v=4/3(pi)r^3 if the diameter is 18 V=4/3π(9)^3 = 643238.64631π

1__0.surface are__ SA=4πr^2 if the radius is 9 SA=4π(81)= 324π