Volume of spheres

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Volume of spheres

  1. 1. Volume of Spheres <ul><li>Starter </li></ul><ul><ul><li>A cone has a diameter of 16m and a slant height of 10m. Find the volume of the cone. </li></ul></ul>April 13, 2010
  2. 2. Review <ul><li>Volume of Square Pyramid </li></ul><ul><ul><li>Related to volume of large cube </li></ul></ul><ul><li>Volume of Cone </li></ul><ul><ul><li>Related to volume of cylinder </li></ul></ul>
  3. 3. Moving on… <ul><li>How can we use the same idea to find the volume of a sphere? </li></ul>
  4. 4. Materials <ul><li>Hemisphere with radius r </li></ul><ul><li>Cylinder with radius r and height 2r </li></ul><ul><li>Cone with radius r and height 2r </li></ul><ul><li>Rice </li></ul>
  5. 5. Procedure <ul><li>Fill the hemisphere with rice. </li></ul><ul><li>Carefully pour the contents of the hemisphere into the cylinder. What fraction of the cylinder does the hemisphere appear to fill? </li></ul><ul><li>Fill the hemisphere again and pour the contents into the cylinder. What fraction of the cylinder do two hemisphere appear to fill? </li></ul>
  6. 6. Procedure <ul><li>If the radius of the cylinder is r and the height is 2r, then what is the volume of the cylinder in terms of r? </li></ul><ul><li>The volume of the sphere is the fraction of the cylinder’s that was filled by two hemispheres. What is the formula for the volume of a sphere? </li></ul><ul><li>The volume of a sphere with radius r is given by the formula: V=4/3 π r 3 </li></ul>
  7. 7. Procedure <ul><li>Fill the hemisphere with rice. </li></ul><ul><li>Carefully pour the contents of the hemisphere into the cone. What fraction of the cylinder does the hemisphere appear to fill? </li></ul>
  8. 8. Procedure <ul><li>If the radius of the cone is r and the height is 2r, then what is the volume of the cone in terms of r? </li></ul><ul><li>What is the formula for the volume of a sphere? </li></ul><ul><li>The volume of a sphere with radius r is given by the formula: V=4/3 π r 3 </li></ul>

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