Question 935256
The diagonal of a solid is an imaginary straight line connecting two vertices of the solid which are not in the same face. Given a cube of edge a:
(a) find the length of its diagonal. 
{{{d = a*sqrt(3)}}}
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(b) find the volume of the waste material made by cutting the largest regular 
cylinder from it.
Vol of the cube = a^3
Not sure what a "regular cylinder" is, but the largest that can be made is:
r = a/2 and h = a
{{{Vol = pi*r^2*h}}}
Waste = a^3 - volume of cylinder.