Question

Find the volume of the indicated region.

the tetrahedron cut off from the first octant by the plane x/8+y/7+z/5=1

Answer 1

hmmmm, if i recall my solid geo, ..lol
at first octant all positive,cutting by the plane
(x/8)+(y/7)+(z/5)=1, in the 3 dimensional space or coordinate
at point x(x,0,0)=(8,0,0), at y(0,y,0)=(0,7,0), and at z(0,0,z)=(0,0,5),
the volume v=a*sqrt2/12 where a=edges if all edges are equal, but here they arent equal
so the volume v=(xy)(xz)(yz))sqrt2/12 xy=sqrt(8^2+7^2)=sqrt113,xz=sqrt(8^2+5^2)=sqrt89, yz=sqrt(5^2+7^2)=sqrt74
v=(sqrt113)(sqrt89)(sqrt74)sqrt2/12
v=101.67 cubic units

Answer 2

thanks alot!