Thursday, May 3, 2012

Comparing Volume & Surface Area (Ch. 12 & 13)

            The surface area and volume formulas for prisms and pyramids & cylinders and cones are actually pretty similar. It's easier if you see the formulas for yourself.

                     Cylinders
       S.A = 2(pi times radius squared) + 2 times pi times radius times height
       V = Pi times radius squared times height

                    Cones
       S.A = L plus B (lateral area plus the area of the base)
       V = 1/3 times pi times radius squared times the height

You can see that to find the volume of both the cylinder and the cone, you have to use pi times radius squared times the height. What's different about the volume between the two is that you have to either multiply by one third or divide by three. 


                   Prisms
 S.A = 2B + Ph (two times the area of the base plus the base's perimeter times the height)
 V = Bh (area of the base times the height)

                  Pyramids
    S.A = L + B (lateral area plus the area of the base)
    V = 1/3 times Bh (area of the base times the height)

You can also see that to find the volume of both the prisms and pyramids, you have to use the area of the base times the height. The only difference is that to find the volume of a pyramid, you have to either multiply by one third or divide by three.