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SURFACE AREA and VOLUME Solid Figures Introduction PRISMS CYLINDERS PYRAMIDS CONES SPHERES APPENDIX

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SURFACE AREA and VOLUME APPENDIX SOLID FIGURES MENU In a previous unit we discussed POLYGONS. POLYGONS are 2-dimensional objects. That means they have length and width, but no depth. Like they are cut out of paper.

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SURFACE AREA and VOLUME APPENDIX SOLID FIGURES MENU In this unit, we will learn about SOLIDS. A SOLID is a 3-dimensional (3D) object. That means it has length, width AND depth.

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SURFACE AREA and VOLUME APPENDIX SOLID FIGURES MENU When the SOLID is made up of POLYGONS, it is called a POLYHEDRON Each POLYHEDRON is made up of Surfaces (called faces) Segments (called edges) Corners (called vertices)

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SURFACE AREA and VOLUME APPENDIX SOLID FIGURES MENU There are many types of solids, we are going to study the 5 basic types: PRISM PYRAMID CYLINDER CONE SPHERE Before we can do anything with SOLIDS, we must understand the difference between these shapes

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SURFACE AREA and VOLUME APPENDIX SOLID FIGURES MENU PRISMS: To create a prism, draw any polygon you like. Next, draw another polygon, just like the first one BASE Connect the corresponding vertices

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SURFACE AREA and VOLUME APPENDIX SOLID FIGURES MENU PRISMS:

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SURFACE AREA and VOLUME APPENDIX SOLID FIGURES MENU PYRAMIDS: Pyramids have one base Instead of connecting to an identical base… They connect to a point. BASE

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SURFACE AREA and VOLUME APPENDIX SOLID FIGURES MENU Pyramids:

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SURFACE AREA and VOLUME APPENDIX SOLID FIGURES MENU When we name prisms and pyramids, we describe the base to tell what kind of prism or pyramid it is. BASEPRISMPYRAMID Triangle Triangular PrismTriangular Pyramid Rectangle Rectangular PrismRectangular Pyramid Pentagon Pentagonal PrismPentagonal Pyramid Hexagon Hexagonal PrismHexagonal Pyramid Heptagon Heptangonal PrismHeptangonal Pyramid Octagon Octagonal PrismOctagonal Pyramid Decagon Decagonal PrismDecagonal Pyramid

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SURFACE AREA and VOLUME APPENDIX SOLID FIGURES MENU CYLINDERS: A cylinder is like a prism… But the bases are circles

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SURFACE AREA and VOLUME APPENDIX SOLID FIGURES MENU Cylinders:

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SURFACE AREA and VOLUME APPENDIX SOLID FIGURES MENU CONES: A cone is a circular pyramid.

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SURFACE AREA and VOLUME APPENDIX SOLID FIGURES MENU Cones:

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SURFACE AREA and VOLUME APPENDIX SOLID FIGURES MENU SPHERES: A sphere is a unique shape... It has no base or sides or edges or vertices.

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SURFACE AREA and VOLUME APPENDIX SOLID FIGURES MENU SPHERES:

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SURFACE AREA and VOLUME APPENDIX SOLID FIGURES MENU Identify each of the following shapes as a PRISM, PYRAMID, CYLINDER, CONE or SPHERE #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 SPHERE CYLINDER PRISM PYRAMID CYLINDERCONEPYRAMID PRISM SPHERECONE & SPHERE

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SURFACE AREA and VOLUME APPENDIX SOLID FIGURES MENU So what are we going to do with these shapes? We are going to calculate SURFACE AREA and VOLUME

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APPENDIX SOLID FIGURES MENU SUFARCE AREA: Is literally the area of all the surfaces of a solid.

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SURFACE AREA and VOLUME APPENDIX SOLID FIGURES MENU SUFARCE AREA: Is literally the area of all the surfaces of a solid.

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SURFACE AREA and VOLUME APPENDIX SOLID FIGURES MENU SUFARCE AREA: Is literally the area of all the surfaces of a solid.

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SURFACE AREA and VOLUME APPENDIX SOLID FIGURES MENU SUFARCE AREA: Is literally the area of all the surfaces of a solid.

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SURFACE AREA and VOLUME APPENDIX SOLID FIGURES MENU VOLUME: Is the measure of how much “space” an object occupies. It is often thought of as how much water an object can hold.

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SURFACE AREA and VOLUME APPENDIX SOLID FIGURES MENU VOLUME: Or how many cubic units it would take to fill an object This is why volume is measured in CUBIC UNITS Like: Cubic feet: ft 3 Cubic centimeters cm 3

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SURFACE AREA and VOLUME APPENDIX PRISMS MENU A prism is a solid with 2 congruent BASES connected by LATERAL FACES Lateral face

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SURFACE AREA and VOLUME APPENDIX PRISMS MENU To find the surface area of a PRISM, you can do it 2 ways: Method 1:Find the area of each shape that makes up the Solid, and add them together The front 2 x 10= The back 2 x 10= 20 The left 6 x 10= 60 The right 6 x 10= 60 The top 2 x 6= 12 The bottom 2 x 6= = 184

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(in a rectangular prism any pair of opposite sides can be bases) SURFACE AREA and VOLUME APPENDIX PRISMS MENU To find the surface area of a PRISM, you can do it 2 ways: Method 2:Use the formula for SURFACE AREA: BASE Identify the BASEs Find the Area and Perimeter of the base B: area of the base P: perimeter of the base h: height of the prism P; 16 A: 12

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SURFACE AREA and VOLUME APPENDIX PRISMS MENU A: 270m 2 6m Find the surface area of this regular decagonal prism: 4m P:60m Find the perimeter of the base =60 Area of the bases Lateral Area

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SURFACE AREA and VOLUME APPENDIX PRISMS MENU Finding Volume is easier! Find the VOLUME of this regular decagonal prism: A: 270m 2 6m 4m P:60m B: area of the base h: height of the prism

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SURFACE AREA and VOLUME APPENDIX PRISMS MENU RIGHT PRISMS vs OBLIQUE PRISMS A right prism is a prism where the lateral faces are all perpendicular to the bases. An oblique prism is a prism where the lateral faces are NOT perpendicular to the bases.

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SURFACE AREA and VOLUME APPENDIX PRISMS MENU SUMMARY: Things you need to know about a prism: A prism has 2 bases All the lateral faces are rectangles Surface Area = 2B + ph B is the area of the base p is the perimeter of the base h is the height of the prism p x h gives the lateral area Volume = B x h B is the area of the base h is the height of the prism

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SURFACE AREA and VOLUME APPENDIX PRISMS MENU Find the… …Surface Area …Lateral Area …Volume 2cm 4cm 3cm A: P: 6cm 2 12cm First we have to find that missing side Use the Pythagorean theorem 4cm 3cm 5cm

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SURFACE AREA and VOLUME APPENDIX PRISMS MENU 4cm 3cm Find the… …Surface Area …Lateral Area …Volume 5cm A: P: 6cm 2 12cm 2cm

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SURFACE AREA and VOLUME APPENDIX PRISMS MENU Find the surface area and volume. Area: Perimeter: ft 2 52ft

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SURFACE AREA and VOLUME APPENDIX PRISMS MENU Find the volume.

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SURFACE AREA and VOLUME APPENDIX PRISMS MENU Archimedes problem.

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SURFACE AREA and VOLUME APPENDIX CYLINDERS MENU Since CYLINDERS are like prisms with circular bases, We need to remember a few basic rules for circles.

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SURFACE AREA and VOLUME APPENDIX CYLINDERS MENU Find the Circumference and area of the circle: 12in 6in The red segment is the DIAMETER We need the RADIUS

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SURFACE AREA and VOLUME APPENDIX CYLINDERS MENU A CYLINDER is like a prism with circular bases The surface area of a cylinder can be found with this formula h: height of the cylinder Most people find this formula easier: Area of the bases Lateral Area B: area of the base C: circumference of the base

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SURFACE AREA and VOLUME APPENDIX CYLINDERS MENU Find the SURFACE AREA of this cylinder:

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SURFACE AREA and VOLUME APPENDIX CYLINDERS MENU The VOLUME of a Cylinder: The VOLUME of a cylinder can be found with this formula h: height of the cylinder The expanded version of the formula: B: area of the base

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SURFACE AREA and VOLUME APPENDIX CYLINDERS MENU Find the VOLUME of this cylinder:

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SURFACE AREA and VOLUME APPENDIX CYLINDERS MENU SUMMARY What you need to know about a cylinder: A cylinder is a prism with circular bases The lateral area is a rectangle Surface Area: Volume: Lateral Area:

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SURFACE AREA and VOLUME APPENDIX CYLINDERS MENU Find the Lateral Area, Surface Area and Volume: 11 mm 9 mm

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SURFACE AREA and VOLUME APPENDIX CYLINDERS MENU Find the surface area and volume of this shape 31 ft 8 ft If it was a complete cylinder: But we only want half of it What did we forget? 31 ft 16 ft

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SURFACE AREA and VOLUME APPENDIX CYLINDERS MENU Find the surface area and volume of this shape 31 ft 8 ft If it was a complete cylinder: But we only want half of it

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SURFACE AREA and VOLUME APPENDIX PYRAMIDS MENU A PYRAMID is a shape with a single base, where all the vertices of the base are connected to a single point (apex)

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SURFACE AREA and VOLUME APPENDIX PYRAMIDS MENU Just like with prisms, we will need to find: Base Perimeter Base Area Height of the pyramid However, with pyramids, we will also need to find a different measurement… …SLANT HEIGHT height Slant height

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SURFACE AREA and VOLUME APPENDIX PYRAMIDS MENU S L A N T H E I G H T Slant height is the distance someone would travel walking up the OUTSIDE of a pyramid.

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SURFACE AREA and VOLUME APPENDIX PYRAMIDS MENU

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SURFACE AREA and VOLUME APPENDIX PYRAMIDS MENU Finding the SURFACE AREA of a PYRAMID B: area of the base P: perimeter of the base L: Slant height Rectangular Pyramid 22m 22m 25m

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SURFACE AREA and VOLUME APPENDIX PYRAMIDS MENU Finding the SURFACE AREA of a PYRAMID Rectangular Pyramid Base Area: Base Perimeter: 484m 2 88m Lateral Area 22m 25m

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SURFACE AREA and VOLUME APPENDIX PYRAMIDS MENU Finding the VOLUME of a PYRAMID B: area of the base h: height Rectangular Pyramid 10ft 8ft 11ft Base Area: Base Perimeter: 80ft 2 36ft

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SURFACE AREA and VOLUME APPENDIX PYRAMIDS MENU SUMMARY: Things you need to know about a pyramid: A pyramid has only 1 base All the lateral faces are triangles Surface Area = B is the area of the base p is the perimeter of the base l is the slant height of the pyramid ½ x p x l is the lateral area Volume = B is the area of the base h is the height of the prism h l

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SURFACE AREA and VOLUME APPENDIX PYRAMIDS MENU Hey, I need to know the height. Hey, I need to know the slant height

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Lateral Area SURFACE AREA and VOLUME APPENDIX PYRAMIDS MENU Find the Lateral Area, Surface area and Volume: B: P:

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SURFACE AREA and VOLUME APPENDIX PYRAMIDS MENU Find the Lateral Area, Surface area and Volume: B: P:

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SURFACE AREA and VOLUME APPENDIX PYRAMIDS MENU Find the Lateral Area, Surface area and Volume: B: P: h

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SURFACE AREA and VOLUME APPENDIX PYRAMIDS MENU Find the Volume:

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SURFACE AREA and VOLUME APPENDIX CONES MENU A CONE is basically a pyramid with a circular base

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SURFACE AREA and VOLUME APPENDIX CONES MENU R H L R: radius H: height L: slant height Lateral Area

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SURFACE AREA and VOLUME APPENDIX CONES MENU 13 12in 5in Find the slant height with the Pythagorean Theorem Find the surface area and volume for the cone shown:

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SURFACE AREA and VOLUME APPENDIX CONES MENU Find the surface area and volume:

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SURFACE AREA and VOLUME APPENDIX CONES MENU Find the Lateral Area: Lateral Area 5

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SURFACE AREA and VOLUME APPENDIX CONES MENU Find the Volume: Cylinder: Cone: TOTAL:

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SURFACE AREA and VOLUME APPENDIX SPHERES MENU A sphere is just a ball. It has 1 important measurement, that is used to find all its other properties The RADIUS R R Official definition of a SPHERE: The collection of all points in space that are the same distance (radius) from a point (center). Official definition of a SPHERE: The collection of all points in space that are the same distance (radius) from a point (center).

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SURFACE AREA and VOLUME APPENDIX SPHERES MENU 12m

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SURFACE AREA and VOLUME APPENDIX SPHERES MENU Find the surface area: 8 in.

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SURFACE AREA and VOLUME APPENDIX SPHERES MENU Find the volume: 2 ft.

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10in SURFACE AREA and VOLUME APPENDIX SPHERES MENU Find the volume and surface area of the hemisphere: Half the sphere + the circle

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10in SURFACE AREA and VOLUME APPENDIX SPHERES MENU Find the volume and surface area of the hemisphere: We only want half

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SURFACE AREA and VOLUME APPENDIX SPHERES MENU Find the volume: Cone: Ice cream: TOTAL:

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SURFACE AREA and VOLUME APPENDIX MENU OPENERS REVIEWS ASSIGNMENTS

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SURFACE AREA and VOLUME OPENERS APPENDIXMENU ABCDEFGHIJKLMNOPQRSTUABCDEFGHIJKLMNOPQRSTU

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SURFACE AREA and VOLUME OPENERS APPENDIXMENU A

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SURFACE AREA and VOLUME OPENERS APPENDIXMENU B

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SURFACE AREA and VOLUME OPENERS APPENDIXMENU C

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SURFACE AREA and VOLUME OPENERS APPENDIXMENU D

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SURFACE AREA and VOLUME OPENERS APPENDIXMENU E

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SURFACE AREA and VOLUME OPENERS APPENDIXMENU F

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SURFACE AREA and VOLUME OPENERS APPENDIXMENU G

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SURFACE AREA and VOLUME OPENERS APPENDIXMENU h

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SURFACE AREA and VOLUME OPENERS APPENDIXMENU I

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SURFACE AREA and VOLUME OPENERS APPENDIXMENU J

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SURFACE AREA and VOLUME OPENERS APPENDIXMENU K

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SURFACE AREA and VOLUME OPENERS APPENDIXMENU L

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SURFACE AREA and VOLUME OPENERS APPENDIXMENU M

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SURFACE AREA and VOLUME OPENERS APPENDIXMENU N

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SURFACE AREA and VOLUME OPENERS APPENDIXMENU O

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SURFACE AREA and VOLUME OPENERS APPENDIXMENU P

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SURFACE AREA and VOLUME OPENERS APPENDIXMENU Q

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SURFACE AREA and VOLUME OPENERS APPENDIXMENU R

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SURFACE AREA and VOLUME OPENERS APPENDIXMENU S

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SURFACE AREA and VOLUME OPENERS APPENDIXMENU T

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SURFACE AREA and VOLUME REVIEWs MENUAPPENDIX

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SURFACE AREA and VOLUME REVIEWs MENUAPPENDIX

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