Prisms: SA= 2B + Ph
V= Bh
Pyramids: SA= B + 1/2Pl or SA= B + LA (LA= 1/2Pl)
V= 1/3Bh or V= Bh/3
Cylinders: SA= 2(pi x r squared) + (2 x pi x r)h
V= pi x r squared x h
Cones: SA= pi x r squared + LA (LA= pi x r x l)
V= 1/3 x pi x r squared x h or V= pi x r squared x h/3
[SA= surface area, B= area of the base, P= perimeter of the base, h= height, V= volume, l= slant length, LA= lateral area, r= radius (the x is a multiplication sign, not a variable)]
The formulas for these 3-D shapes can be compared and contrasted by looking at many different qualities. First of all, each volume formula involves having to find the area of the area of the base of the object. Both cylinders and cones implement the use of pi because their bases are circles; however, any shape that does not contain a circle will not need to use pi in its formula. To find the volume of cones and pyramids, one must multiply by one-third (or divide by three) to find the value because each shape is a third of either the prism or cylinder. Also, all of the formulas use height, or slant height for cones and pyramids. Finally, the formulas are different because each has to conform to the different angles and properties of the shapes; for instance, since the bases of cones and cylinders are circles, one's volume and surface area measurements will not be exact. This is because pi is infinite and does not terminate. This, however, does not apply to prisms or pyramids because they are not involved with circles. These are only some similarities and differences between these formulas and their shapes.
