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Volume of Spheres and Cones - Math Lesson

This math lesson covers the volume of spheres and cones. Students will learn to write equations, solve equations, and calculate surface area. Worksheets and interactive tools are provided.

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Volume of Spheres and Cones - Math Lesson

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  1. Math CC7/8 – Be Prepared Unit: Filling and Wrapping Journal: • Date: 3/6/2019 • Title: 4.4 Spheres and Cones 3) Correct then have a Neighbor Sign off on HW from last night (p.83) 4) Warm Up: Use this equation: On Desk: Turn In:1) (If not done yet: SKILL RATIOS & PROPORTION HW) 2 3 y = x - 4 1) Write an equation for a line that is parallelto the line in the equation. 2) What is the value of y, if x = -18 ? In Your Planner: HW: p. 85, #10-13, 20-21 WDYE Retake –Fri 3/8 FW Test: Mon 3/11 & Tues 3/12 - No Retake, V&SA Wheel notes -okay!

  2. Tasks for Today • Warm up • Lesson 4.4 - Vol. of Cones & Spheres • Begin HW?

  3. Warm Up (no calculator!) Write an equation for a line that is parallel to the line In the equation what is the value of y, if x = - 18 ? Same slope, different y-intercept! y = - 16 2 3 2 3 Solve the equations. y = x - 4 y = x - 4 q + 14 = 8(q + 7) q = -6 y = 58 • 12(y + 5) = 13y + 2

  4. SA of Cylinder • Sketch a cylinder with a height of 15in and a diameter of 5in. What is the SA of this Cylinder? • Work together in your group. You have 5 minutes.

  5. The cylinder with the larger base has a larger volume The cylinder with the greater height has a smaller volume.

  6. The cylinders have different areasof the base (B) and different heights, so the volumes will be different. So… if you build 2 cylinders from the same rectangle, the one with the larger base will have the greatest volume. Begin HW : p. 83, #3, 4 – volume only, 7a, 30 – 34

  7. Interactive Tools PBS Learning – Cylinders, Spheres, & Cones CMP3 – Pouring & Filling

  8. A sphere is 2/3 the volume of a cylinder … with the same diameter and height. A cone is 1/3 the volume of a cylinder… with the same diameter and vertical height.

  9. Diameter of 3 in. A sphere is 2/3 the volume of a cylinder with the same diameter and height. Cylinder Sphere V = (3.14) (r) (r) (h) V = V = (volume of cylinder) Skip #3 - 4

  10. A cone is 1/3 the volume of a cylinder… with the same diameter and vertical height. V =

  11. The volume increases very rapidly as the radius increases. What patterns do you see in how the volume grows as the radius increases? When the radius is doubled, how does the volume increase? When the radius is doubled, the volume increases by a factor of 8! When the radius is tripled, the volume increase by a factor of 27! How is the effect of scaling up the radius similar to the patterns you noticed when you scaled up rectangular prisms?

  12. V = 64 cubic in. V = V = V = 42 and 2/3 cubic in. V = 21 and 1/3 cubic in.

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