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integration in multiple dimensions

Using integration over space, is it possible to derive the formulae for the SA of a sphere, and for the volume of a square based pyramid? And how is it done?

Reply 1

Zacken

Sure, just integrate 1 over the surface of the sphere.

Reply 2

RichE

If you go to chapters 5 and 6 of this

https://courses.maths.ox.ac.uk/node/view_material/475

you'll see how surface areas can be calculated.

The square pyramid could either be done as a triple integral or as a single integral, integrating the cross-sectional area with respect to height.