Math 310

1
Math 310

• Section 11.5
• Volume

2
Volume

• Like length, and area, volume measures the
  physical space we reside in, now just in 3
  dimensions.
• Just as in surface area, we are going to look at
  some basic formulas for common figures.

3
Common Figures and Formulas

• Prisms and Cylinders
• Pyramids and Cones
• Spheres

4
Prisms and Cylinders

• For both of these figures, the basic idea is to
  find the area of the base, and then multiply by
  the height. Sounds easy but the trick is often
  correctly identifying the base.
• V ABh

5
Ex
6
Pyramids and Cones

• Although very similar to prisms and cylinders,
  the volume of a pyramid or cone is found by
  finding the area of the prism or cylinder that it
  would fit into, and then multiplying by the
  appropriate fraction.
• V ABh(1/3)

7
Ex
8
Spheres

• The sphere, like the cylinder or cone, is simply
  a fraction of a larger figure. Specifically, a
  sphere is 2/3 the volume of a cylinder it fits
  exactly into.
• V (2/3) pr2 2p
• (4/3)pr3

9
Ex
10
And again

• Just as with surface area, we can now put them
  all together and find volumes of more complex
  figures.

11
Ex