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VeJo23 Chapter 9 Link


 * __Chapter 7, Surface Area and Volume.__**

7.1 Surface area and Volume.



Surface area: The surface area if n object is the total area of the exposed surfaces. Volume: the volume is the amount of cubic units that can fit in any one shape. Surface area of a rectangular prism: S= Surface area V= Volume. S=2LW+2WH+2LH V=LWH Surface area of a cube: S=6S^2 V=S^3 Examples: What is the volume and surface area of the following rectangular prisms. L=12 W=15 H=3 V= S=_

L=6 W=13 H=4 V= S=_

L=13 W=17 H=9 V=_ S=_

Find the volume and surface area of the following cubes.

SL=5 V=

SL=7 V=

SL=3 V=

7.2 The Surface Area and Volume of Prisms.



Altitude:This is the segment that conects the 2 planes tha make up the top and the bottom of the prism. Height: it is the length of the altitude.

Surface are of a right prism: S= surface area L=lateral area B= base area P= perimeter H= height S=L+2B or S= HP+2B

Cavaliers Principle: If to solids with the smae top and bottom plane at the same height, they have the same area.

Volume of a prism: V= volume h= height B= base V=BH

Examples:

V= if H=12 and B=5

V= if H=16 and B=23

V= if H=32 and B=23

7.3 Surface area and Volume of Pyramids.



A pyramid is a polyhedron with base with 3 or more sides and three or more lateral faces that are tryangles that share a vertex. Lateral edge: The intersection of two lateral faces. base edge: it is the two edges of the lateral face and base that intersect and with eachother. Vertex of a pyramid: the length between the vertex and the base plain. height of a pyramid: it is the legth of the alltitude. Regular pyramid: it is a pyt\rimid with a regular polygon as a base and all the lateral faces are equal. Slant height: this is the length of the altitude of the lateral face

Surface area of a regular Pyramid: surface area= S Lateral area=L Base area=B Perimeter of base=P Slant height=L S=L+B or S=1/2LP+B.

Volume of a Pyramid: Volume=V Height=H Base area=base V=1/2BH.

V= SA= S=26 L=28 B=25 L=12

V= if B=25 and H= 5

V= if B=36 and H=6

7.4 Surface area and volume of cylinders.



Cylinder: A solid with two circle bases on perpindicular planes conected by a solid. Lateral Surface: the part conecting the two circles. the base of a cylinder: the two circle chapes on perpindicular planes that are the top and bottom of the cylinder. Altitude: the distant between the two bases. Height: the length of the altitude. Axis of a cylinder: it is the segment that is conecting the centers of the two bases. Right cylinder: a cylinder is a right cylinder if the base ad the axis make a 90 degree angle. Oblique cylinder: a cylinder that the base and axis do not form a 90 degrees.

Surface Area of a Right Cylinder: S=Surface Area L=Lateral area B=Base Area R=Radius H=Height P=Pi S=L+2B or S=2PRH+2PR^2

Volume of a cylinder: V=Volume R=Radius H=Height B=Base area P=Pi V=BH or V=PR^2H

7.5 Surface Area and Volume of Cones.



Cone: A 3 dimeninal figure witha single circular bade with a rounded lateral surface that goes up to a vertex. Right Cone: A right cone is when the center of thebase and he vertex form a 90 degree angle. Oblique Cone: If its not a right cone than its an Oblique.

Surface are of a right cone: Surface Area= S Lateral area=L Base area=B Radius=R Slant height=L S=L+B

Volume of a cone: Volume=V Radius=R Height=H Base Area=B V=1/3BH

7.6 Suface Area and Volume of Spheres.



Sphere: An object that has the exact same length everywhere from the center of the shape.

Volume of a Sphere: V=Volume R=Radius P=Pi V=4/3PR^3

Surface Area of a Sphere: S=Surface Area R=Radius P=Pi S=4PR^2

Chapter Examples:

Triangular prisms: Find the volume of a right triangular prism with the dimentions A= 5 un. B=6 un.and C=12 un. A*B =5*6= 30 (A*B)*C =(30/2)*12= 360 un^3

Find the surface area of this same triangular prism. A*B =5*6= 30 B*C =6*12= 72 A*C =5*12= 60 a^2+b^2=H^2 H*C =7.81*12= about 93.7 93.7+60+72+30=255.7 SA=255.7

Find the Volume of this Pyramid:



if the base has an area of 25 and hieght is 6 V=1/2BH= 1/2(25*6)=75 V=75

Find the surface area of a pyramid with the dimentions: P=20 L=6.5 B=25

S=1/2LP+B=1/2(6.5*20)+25=90 SA=90

Volume of a cylinder: Find the volume of a cylinder with the dementions of R=5 and H=6

V=PR^2=P(5)(6)^2=565.46

Find the surface area of a cylinder with the same dimentions: p=15.7

2PRH+2PR^2=2(15.7)(5)(6)+2(15.7)(5)^2=1727

Volume of Cones: Find the volume of a cone with the dimentions B=5 H=6

V=1/3BH=1/3(5)(6)=10

Volume of a Sphere: Find the volume of a sphere with the dimentions R=5 V=4/3PR^3=4/3P5^3=523.59

Surface Area of a Sphere: Find the SA of a sphere with the same dimentions: S=4PR^2=4P5^2=314.15