A triangular pyramid and a triangular prism have the same base and height. The volume of the prism is how many times the volume of the pyramid?

Question

I don't know what it means.

↳Redirected from "How do I change #int_0^1int_0^sqrt(1-x^2)int_sqrt(x^2+y^2)^sqrt(2-x^2-y^2)xydzdydx# to cylindrical or spherical coordinates?"

8841 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-20T02:23:30

The volume of the prism is three times that of the volume of the pyramid.

Let #V_(pyr)# = the volume of the pyramid.

Let #V_(pris)# = the volume of the prism.

We know that

#V_(pyr)=1/3xx# area of base #xx# height

and

#V_(pris)=# area of base #xx# height

The problem is asking for the ratio

#V_(pris)/V_(pyr)=1/(1/3)=3#

because the area of the base and the height cancel out.