volume learning about

There are three classes of solid that we will look at: Prisms Tapered Solids Spheres

Prisms Solids that have a uniform cross- section. Toothpaste squeezed from a tube is a prism, as are cylinders and cubes. To find the volume of a prism, calculate the area of the cross-section, and multiply by the prism’s length.

Tapere d Solids Solids that have a flat base, of ANY shape, that rises to a single point. Pyramids and cones are tapered solids with regular bases. To make a tapered solid from a prism, you end up removing 2 / 3 of the mass of the prism - this does not change wherever the point of the taper meets the end of the prism. V = (area x height) 3

Sphere s Solids that have a uniform circular cross-section in all orientations. If we fit a sphere in its cube, each cube side = 2 x radius. The cube then has a volume of r 3 x 8. 8 ≈ 2.55, so cube = 2.55 r 3 The sphere is about ½ the volume of the cube; 2.55 ÷ 2 = 1.275, a bit less than 4 / 3, so V = 4r 3 3