Math 310 Section 11.5 Volume

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.

Common Figures and Formulas Prisms and Cylinders Prisms and Cylinders Pyramids and Cones Pyramids and Cones Spheres Spheres

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 = A B h

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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 = A B h(1/3)

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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)· πr 2 · 2π = (4/3)πr 3 = (4/3)πr 3

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And again… Just as with surface area, we can now put them all together and find volume’s of more complex figures.

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