volume

learning about

There are three classes of solid that we will look at:

Prisms

Tapered Solids

Spheres

PrismsSolids 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.

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Tapered

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

Spheres

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 r3 x 8.8 ≈ 2.55 , so cube = 𝜋2.55 r𝜋 3

The sphere is about ½ the volume of the cube; 2.55 ÷ 2 = 1.275, a bit less than 4/3, so

V = 4 r𝜋 3

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