Volume of Spheres

1
Volume of Spheres

• Using the model of a collection of pyramids that
  are joined at their vertex, we can visualize the
  creation of a sphere. The junction of the
  vertices forms the center of the sphere. The
  bases of the pyramids form the surface area of
  the sphere. The height of the pyramid becomes
  the radius of the sphere.

2
Volume of Spheres

• Thus, if we consider the volume of the sphere to
  be the sum of the volume of the pyramids, then
• V (1/3)Bh
• becomes
• V (1/3)(4?r2)r
• (4/3)?r3

3
Example 3-1d
4
Example 3-2b
Find the volume of the hemisphere.
5
Example 3-3c
Short-Response Test Item Compare the volumes of
the hemisphere and the cylinder with the same
radius and height as the radius of the hemisphere.
6
Example 3-3d