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Honors Geometry 22/23 February 2012

Honors Geometry 22/23 February 2012. Warm Up 1. A tall fir tree casts a shadow that measures 8 ½ yards at the same time a six foot man casts a 2 ½ foot shadow. What is the height of the fir tree? a) 20.4 ft b) 61.2 ft c) 63.75 ft d) 153 ft

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Honors Geometry 22/23 February 2012

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  1. Honors Geometry 22/23 February 2012 Warm Up 1. A tall fir tree casts a shadow that measures 8 ½ yards at the same time a six foot man casts a 2 ½ foot shadow. What is the height of the fir tree? a) 20.4 ft b) 61.2 ft c) 63.75 ft d) 153 ft Show your work and explain how you know you are correct. 2. Find r if C = a) 8.5 in b) 11 in

  2. Objective Students will find surface area and volume of various figures. Students will take notes, participate in class discussion and use think-pair-share.

  3. due TODAY HW grade: TEST CORRECTIONS FORMAT: 1) Explain what you did incorrectly 2) rework the problem correctly showing all steps 3) ATTACH corrections to test paper DO pg. 533: 1, 7, 12 Due February 24 Worksheet SA of Cylinders and Cones # 1- 6, 9, 10, 12, 13- show work on separate paper

  4. VOLUME and SA BASICALLY, SA = AREAbase(s) + LSA (add the areas of the faces) VPRISM/CYLINDER = ABASE x HEIGHT HEIGHT is ALWAYS PERPENDICULAR distance

  5. Which has more volume?more surface area? You can make two different cylinders by rolling a piece of notebook paper either “longways or shortways”. WHICH SHAPE HAS MORE VOLUME? WHICH SHAPE HAS MORE Surface Area? (including the bases?) Can you explain why? 

  6. Geometric Solids 2 Bases1 BaseNo Base Prisms & Cylinders Cones & pyramids Spheres Bases are congruent and parallel

  7. Volume = Surface Area • The measure of the amount of space contained in a solid • The ‘inside’ of the geometric figure • Use volume formulas • measured in cubic feet, cubic inches… • COUNT CUBES • The sum of the areas of all the faces • The ‘outside’ of the geometric figure • Use area formulas • Measured in square inches, square feet… • COUNT SQUARES

  8. Oblique Rectangular Prism Altitude = height

  9. Altitude Right Cylinder Oblique Cylinder Altitude = height

  10. Volume

  11. Volume BASE is a TRAPEZOID! PRISMS have TWO bases that are PARALLEL and CONGRUENT V = Abase∙H = ½ (b1 + b2) h ∙ H V = ½ (10 + 34) (6) (20) = 2640 u3

  12. Volume Rectangular Prism V = Abase∙ H Trapezoidal prism Triangular prism

  13. what about a cone? DEMONSTRATION--- How many “conefuls” of water will it take to fill a cylinder of the same radius and height? same height same volume? congruent bases

  14. what about a pyramid? DEMONSTRATION--- How many “pyramids-fuls” of water will it take to fill a prism with same base area and height? same height same volume? same base area

  15. Volume Trapezoidal prism Rectangular Prism V = Abase∙ H Cylinder Prism Study Sheet Triangular prism Pyramid Cone V = 1/3 Abase∙ H V = 1/3 Abase∙ H

  16. practice Complete problems on handout. Be prepared to share them with the class. You have 25 minutes. This work will be collected for a classwork grade.

  17. debrief how is volume different that surface area? how do you find the surface area of a cone? how did we find the volume formula for a cone? a pyramid?

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