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# 11.3 and11.5 Surface Area and Volume Pyramids

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### Transcript

• 1. Chapter 11 Surface Area and Volume 11.3 and 11.5 S
• 2. Essential UnderstandingS To find the surface area of a 3D figure, find the sum of the areas of all the surfaces of the figureS The volume of a pyramid is related to the volume of a prism with the same base and heightS The volume of cone is related to the volume of a cylinder with the same base and height
• 3. ObjectivesS Students will be able to S Find the surface area of a pyramid and a cone S Find the volume of a pyramid and of a cone
• 4. PyramidsS Pyramid: polyhedron in which one face (the base) can be any polygon and the other faces (lateral faces) are trianglesS Vertex: top of pyramidS Slant height: length of the altitude of a lateral face of the pyramidS Assume a pyramid is a regular pyramid unless otherwise stated
• 5. LA and SA of PyramidsS Lateral Area (LA): sum of the areas of the congruent lateral faces S Half the product of the perimeter and the slant height S LA = ½ plS Surface Area (SA): add the area of the base to the lateral area. S SA = LA + B S SA = ½ pl + BS When the slant height is not given you must find it first in order to find the LA or the SA
• 6. What is the Surface Area
• 7. What is the lateral area?
• 8. Volume of a PyramidS V = 1/3 Bh
• 9. ConeS Base is a circleS Right Cone: altitude is a perpendicular segment form the vertex to the center of the baseS Height is the altitudeS Slant Height: distance from the vertex to a point on the edge of the base
• 10. LA and SA of a ConeS Lateral Area (LA): half the product of the circumference of the base and the slant height S ½ * 2πr * l = S πrlS Surface Area (SA): sum of the lateral area and the base S LA + B S πrl + πr2
• 11. What is the surface area in terms of pi?
• 12. Volume of a ConeS V = 1/3BhS V = 1/3 π r2 h
• 13. HomeworkS Pg. 713S #10 – 22 even, 28 (8 problems)S Pg. 729S #6 – 18 even, 30 (8 problems)S 16 problems total