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## SURFACE AREA and VOLUME

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**SURFACE AREA and VOLUME**Solid Figures Introduction CYLINDERS PRISMS PYRAMIDS SPHERES CONES APPENDIX**SURFACE AREA and VOLUME**SOLID FIGURES 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. APPENDIX MENU**SURFACE AREA and VOLUME**SOLID FIGURES In this unit, we will learn about SOLIDS. A SOLID is a 3-dimensional (3D) object. That means it has length, width AND depth. APPENDIX MENU**SURFACE AREA and VOLUME**SOLID FIGURES 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) APPENDIX MENU**SURFACE AREA and VOLUME**SOLID FIGURES Before we can do anything with SOLIDS, we must understand the difference between these shapes There are many types of solids, we are going to study the 5 basic types: PRISM PYRAMID CYLINDER CONE SPHERE APPENDIX MENU**SURFACE AREA and VOLUME**SOLID FIGURES To create a prism, draw any polygon you like. PRISMS: Next, draw another polygon, just like the first one Connect the corresponding vertices BASE BASE BASE APPENDIX MENU**SURFACE AREA and VOLUME**SOLID FIGURES PRISMS: APPENDIX MENU**SURFACE AREA and VOLUME**SOLID FIGURES PYRAMIDS: Pyramids have one base Instead of connecting to an identical base… They connect to a point. BASE BASE BASE APPENDIX MENU**SURFACE AREA and VOLUME**SOLID FIGURES Pyramids: APPENDIX MENU**SURFACE AREA and VOLUME**SOLID FIGURES When we name prisms and pyramids, we describe the base to tell what kind of prism or pyramid it is. APPENDIX MENU**SURFACE AREA and VOLUME**SOLID FIGURES CYLINDERS: A cylinder is like a prism… But the bases are circles APPENDIX MENU**SURFACE AREA and VOLUME**SOLID FIGURES Cylinders: APPENDIX MENU**SURFACE AREA and VOLUME**SOLID FIGURES CONES: A cone is a circular pyramid. APPENDIX MENU**SURFACE AREA and VOLUME**SOLID FIGURES Cones: APPENDIX MENU**SURFACE AREA and VOLUME**SOLID FIGURES SPHERES: A sphere is a unique shape... It has no base or sides or edges or vertices. APPENDIX MENU**SURFACE AREA and VOLUME**SOLID FIGURES SPHERES: APPENDIX MENU**SURFACE AREA and VOLUME**SOLID FIGURES Identify each of the following shapes as a PRISM, PYRAMID, CYLINDER, CONE or SPHERE #1 #2 #3 #4 SPHERE CYLINDER PRISM #5 #6 PYRAMID #7 CYLINDER CONE PYRAMID #9 #10 #8 SPHERE CONE & SPHERE PRISM APPENDIX MENU**SURFACE AREA and VOLUME**SOLID FIGURES So what are we going to do with these shapes? We are going to calculate SURFACE AREA and VOLUME APPENDIX MENU**SURFACE AREA and VOLUME**SOLID FIGURES SUFARCE AREA: Is literally the area of all the surfaces of a solid. APPENDIX MENU**SURFACE AREA and VOLUME**SOLID FIGURES SUFARCE AREA: Is literally the area of all the surfaces of a solid. APPENDIX MENU**SURFACE AREA and VOLUME**SOLID FIGURES SUFARCE AREA: Is literally the area of all the surfaces of a solid. APPENDIX MENU**SURFACE AREA and VOLUME**SOLID FIGURES SUFARCE AREA: Is literally the area of all the surfaces of a solid. APPENDIX MENU**SURFACE AREA and VOLUME**SOLID FIGURES VOLUME: Is the measure of how much “space” an object occupies. It is often thought of as how much water an object can hold. APPENDIX MENU**SURFACE AREA and VOLUME**SOLID FIGURES 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: ft3 Cubic centimeters cm3 APPENDIX MENU**SURFACE AREA and VOLUME**PRISMS A prism is a solid with 2 congruent BASES connected by LATERAL FACES Lateral face APPENDIX MENU BASE**SURFACE AREA and VOLUME**PRISMS 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 = 20 12 The back 2 x 10 = 20 The left 6 x 10 = 60 10 60 The right 6 x 10 = 60 20 The top 2 x 6 = 12 The bottom 2 x 6 = 12 6 = 184 2 APPENDIX MENU**SURFACE AREA and VOLUME**PRISMS To find the surface area of a PRISM, you can do it 2 ways: Method 2: Use the formula for SURFACE AREA: • Identify the BASEs (in a rectangular prism any pair of opposite sides can be bases) • Find the Area and Perimeter of the base BASE P; 16 A: 12 10 h: height of the prism B: area of the base 10 6 P: perimeter of the base 2 12 16 APPENDIX MENU**SURFACE AREA and VOLUME**PRISMS Find the surface area of this regular decagonal prism: Find the perimeter of the base 6+6+6+6+6+6+6+6+6+6 =60 Area of the bases Lateral Area A: 270m2 P:60m 6m 4m APPENDIX MENU**SURFACE AREA and VOLUME**PRISMS Finding Volume is easier! Find the VOLUME of this regular decagonal prism: h: height of the prism B: area of the base A: 270m2 P:60m 6m 4m APPENDIX MENU**SURFACE AREA and VOLUME**PRISMS 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. APPENDIX MENU**SURFACE AREA and VOLUME**PRISMS 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 APPENDIX MENU**SURFACE AREA and VOLUME**PRISMS Find the… 3cm …Surface Area 4cm 2cm …Lateral Area First we have to find that missing side 3cm 4cm …Volume Use the Pythagorean theorem 5cm A: P: 6cm2 12cm APPENDIX MENU**SURFACE AREA and VOLUME**PRISMS Find the… …Surface Area 3cm 4cm 5cm 2cm …Lateral Area …Volume A: P: 6cm2 12cm APPENDIX MENU**SURFACE AREA and VOLUME**PRISMS Find the surface area and volume. 10 8 112 24 14 6 Area: Perimeter: 136ft2 52ft APPENDIX MENU**SURFACE AREA and VOLUME**PRISMS Find the volume. APPENDIX MENU**SURFACE AREA and VOLUME**PRISMS Archimedes problem. APPENDIX MENU**SURFACE AREA and VOLUME**CYLINDERS Since CYLINDERS are like prisms with circular bases, We need to remember a few basic rules for circles. APPENDIX MENU**SURFACE AREA and VOLUME**CYLINDERS Find the Circumference and area of the circle: 6in 12in The red segment is the DIAMETER We need the RADIUS APPENDIX MENU**SURFACE AREA and VOLUME**CYLINDERS 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 B: area of the base Area of the bases Lateral Area C: circumference of the base Most people find this formula easier: APPENDIX MENU**SURFACE AREA and VOLUME**CYLINDERS Find the SURFACE AREA of this cylinder: APPENDIX MENU**SURFACE AREA and VOLUME**CYLINDERS The VOLUME of a Cylinder: The VOLUME of a cylinder can be found with this formula h: height of the cylinder B: area of the base The expanded version of the formula: APPENDIX MENU**SURFACE AREA and VOLUME**CYLINDERS Find the VOLUME of this cylinder: APPENDIX MENU**SURFACE AREA and VOLUME**CYLINDERS 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: APPENDIX MENU**SURFACE AREA and VOLUME**CYLINDERS Find the Lateral Area, Surface Area and Volume: 11mm 9mm APPENDIX MENU**SURFACE AREA and VOLUME**CYLINDERS Find the surface area and volume of this shape 31ft 8ft 16ft 31ft If it was a complete cylinder: What did we forget? But we only want half of it APPENDIX MENU**SURFACE AREA and VOLUME**CYLINDERS Find the surface area and volume of this shape 31ft 8ft If it was a complete cylinder: But we only want half of it APPENDIX MENU**SURFACE AREA and VOLUME**PYRAMIDS A PYRAMID is a shape with a single base, where all the vertices of the base are connected to a single point (apex) APPENDIX MENU**SURFACE AREA and VOLUME**PYRAMIDS 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… height Slant height …SLANT HEIGHT APPENDIX MENU**SURFACE AREA and VOLUME**PYRAMIDS Slant height is the distance someone would travel walking up the OUTSIDE of a pyramid. SLANT HEIGHT APPENDIX MENU**SURFACE AREA and VOLUME**PYRAMIDS APPENDIX MENU