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Geometry November 13, 2013

Geometry November 13, 2013. Today’s Question: How do we find the volume of cylinders, prisms, cones, and pyramids? Standard: MMC9-12.G.GMD1 and 3. Which of these are volumes?. A gallon An acre A liter A square meter A cubic foot A barrel full A truck load A metric ton A teaspoon

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Geometry November 13, 2013

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  1. GeometryNovember 13, 2013 Today’s Question: How do we find the volume of cylinders, prisms, cones, and pyramids? Standard: MMC9-12.G.GMD1 and 3

  2. Which of these are volumes? • A gallon • An acre • A liter • A square meter • A cubic foot • A barrel full • A truck load • A metric ton • A teaspoon • A lightyear

  3. Volume of Prisms &Cylinders

  4. VOLUME has cubic units Cm3, ft3, units3 VOLUME = the number of cubic units contained in its interior

  5. Volume = length•width•height In a CUBE they are all the same The volume of a cube is side3 Volume = s3 4 ft Volume = 43 Volume = 64 ft3

  6. What is a prism?

  7. Definition of a Prism • A prism is a “polyhedron” with two congruent faces, called bases, that lie in parallel planes. The other faces are called lateral faces. • A polyhedron is any solid bounded by polygons, referred to as faces.

  8. When a prism is NOT a cube… B(area of the BASE) The formula for B will depend on the shape of the base.

  9. Volume Formula for Prisms & Cylinders V = Bh

  10. Volume of a Prism B = area of the BASE h = HEIGHT 4 in 3 in 2 in V = 12 in3

  11. Volume of a Cylinder 7 cm 5 cm Round to the nearest tenth. V = 769.7 cm3

  12. You try! Find the volume. • A cylinder has a radius of 5 cm and a height of 8 cm. Sketch the cylinder and label its dimensions, then find the volume. State your answer both in terms of πand as a decimal rounded to the nearest hundredth.

  13. Try Another! • A cube has a volume of 343 cubic meters. What is the length of a side of the cube? x x x

  14. Homeworkp. 746-747nos. 13-18, 25-30

  15. Ticket Out the door • You need to buy a container that holds as much liquid as possible for water storage. You go to Home Depot and they offer two different containers, one cylindrical and the other a rectangular prism. They are both 3.5’ tall. The rectangular prism’s base is 30” x 30” and the cylinder’s diameter is 30”. They are the same price. Which do you buy? Justify your answer.

  16. GeometryNovember 14, 2013 Today’s Question: How do we find the volume of cylinders, prisms, cones, and pyramids? Standard: MMC9-12.G.GMD1 and 3 MMC9-12.G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. MMC9-12.G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

  17. Volume of Pyramids and Cones

  18. Opener What is the volume of the cylinder with a diameter of 40 mm and a height of 112 mm? Use the correct units!

  19. Homework Answers • 512 in3 • 240 cm3 • 318.26 in3 • 6785.84 m3 • 288.40 ft3 • 381.00 cm3 • 924 m3 • 628.32 ft3 • 116.91 cm3 • u = 10 ft • v = 13.92 yds • w = 4 cm

  20. #15- Challenge Problem

  21. Measuring with Millimeters There are 25.4 mm per inch. Measure the diameter and the height of the cone to the nearest millimeter.

  22. How many cones will it take to fill the cylinder? If: • They have the same size base. • They also have the same height.

  23. Volume Formula for Cones & Pyramids

  24. Find the volume. 8 ft 10 ft 12 ft

  25. Find the volume! Base dimension are 6’ x 8’ and the height is 12’ Volume = ?

  26. Find the volume! The cone’s radius is 12 mm and its height is 20 mm. Volume = ?

  27. Find the Missing Dimension! The pyramid’s base is 20’x 20’. The volume of the pyramid is 8000 cubic feet. What is its height?

  28. What is the volume of this cone? Round to the nearest tenth. 3.6 cm 3 cm 2 cm

  29. Ticket Out the Door! • A cone and a pyramid have the same volume and the same height. If the pyramid’s base is 12’ x 10’, what is the radius of the base of the cone?

  30. HomeworkHandout from Geometry book p. 755-756,nos. 8-14 and 17-22

  31. Surface Area and Volume of Spheres

  32. 2 Types of Answers Rounded • Type the Pi button on your calculator • Toggle your answer • Do NOT write Pi in your answer Exact • Pi will be in your answer

  33. Radius of a Sphere r

  34. If you cut a sphere right down the middle you would create two congruent halves called HEMISPHERES. You can think of the globe. The equator cuts the earth into the northern and southern hemisphere.

  35. Look at the cross section formed when you cut a sphere in half. What shape is it? A circle!!! This is called the GREAT CIRCLE of the sphere.

  36. Surface Area of a Sphere

  37. Surface Area of a Sphere (round to the nearest hundredths) 8 in

  38. Surface Area of a Sphere (round to the nearest hundredths) 10 cm

  39. The circumference of a great circle of a sphere is 25 inches. Find the surface area of the sphere. (Round to the nearest tenths.) 25 in

  40. A sphere is inscribed in a cube of volume 27 cubic meters. What is the surface area of the sphere? Give an exact answer and an answer rounded to the nearest hundredth.

  41. Volume of a Sphere

  42. Volume of a Sphere (round to the nearest hundredths) 2 cm

  43. Volume of a Sphere (round to the nearest hundredths) 10 cm

  44. Volume of a Sphere A sphere is inside a cube. The cube has a volume of 27 cm3. Find volume of the sphere. Round to the nearest hundredths.

  45. WS9– 16

  46. Homework Worksheet

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