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13.3 - Volume of a Sphere!

13.3 - Volume of a Sphere! . Volume Formula of a Sphere:. In 3 dimensions, the  volume  inside a sphere is found by using the formula where r  is the radius of the sphere. Once you have the radius, you can easily find Volume! . Math History:.

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13.3 - Volume of a Sphere!

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  1. 13.3 - Volume of a Sphere!

  2. Volume Formula of a Sphere: In 3 dimensions, the volume inside a sphere is found by using the formula wherer is the radius of the sphere. Once you have the radius, you can easily find Volume! 

  3. Math History: Archimedes first derived this formula, which shows that the volume inside a sphere is 2/3 that of a circumscribedcylinder.  • It’s important to note that the sphere and the cylinder have the same radius and the same height/diameter! 

  4. I’m curious… Let’s see how this works! Vcylinder = (πr²)•H Vcylinder = (πr²)•2r Vcylinder = 2πr³ Vsphere = 2/3 • Vcylinder Vsphere = 2/3 • (2πr³) Vsphere = 4/3 • (πr³)

  5. Let’s watch how this works! http://www.youtube.com/watch?v=h4j8l3p22e8

  6. Fun Facts! • A spherical triangle is a figure formed on the surface of a sphere by three great circular arcs intersectingin three vertices. • The spherical triangle is sometimes called an Euler (oiler) triangle. • The sum of the angles of a spherical triangle are between 180°- 540°. For a given surface area, the sphere is the one solid that has the greatest volume. This why it appears in nature so much, such as water drops, bubbles and planets.

  7. M.C. Escher Self-Portrait

  8. A group of students from the Charles W Davidson College Of Engineering at San Jose State University worked on an omnidirectional, self-balancing SDS electric motorcycle. [September 14, 2012] The SDS concept vehicle is described as a self-balancing electric motorcycle that rides on spheres. Rather than using the kind of mechanical gyros that help keep the gyrobikein an upright position, the SDS creation uses data from MEMS gyroscopic sensor technology and an onboard accelerometer to electronically control balance.

  9. Example #1: Find the exact volume of a sphere that has a diameter of 18 cm

  10. Example #2: Find the exact volume of the sphere…

  11. Example #3: Find the exact volume of the hemisphere…

  12. Example #4: If the exact volume of a sphere is 36π cubic inches (in³), find its diameter and its radius.

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