0

Compute the area of the region cut from the plane $x+y+z = a$ by the cylinder $x^2 +y^2 = a^2$.

The solution I am reading is here. I understand how they parametrized $x$ and $y$ in $r(u,v)$, but why is the parameterization of $z$ equal to $a−u \cos v−u \sin v$?

Euclid
  • 45
  • 7

1 Answers1

0

They use cylindrical coordinates

$$x=u\cos v,\\y=u\sin v$$ because the equation of the cylindre becomes simply $$u=a.$$

The equation of the plane is a mere substitution

$$u\cos v+u\sin v+z=a.$$