# Which is the area of each faces for the rectangular prism.

1. Sep 17, 2008

### germana2006

1. The problem statement, all variables and given/known data

Considering a rectangular prism bounded by six rectangular faces (x=2, y=0.5,
z=1) and a cylinder (r=0.5, heigh h=2) that cut the rectangular prism in x=1
y=0 and z=0 with a inclination of 45 grads in y and z. Which is the area of
each faces for the rectangular prism. I need not the numerically solutions but
the analytically solution.

2. Relevant equations

3. The attempt at a solution

The area of each face of a rectangular prism is Ar=a*b but now I must rest the
area of the cylinder. The cylinder area is known as Ac=2*pi*r*h. But this is
not the result. If the rectangular prism would be a cube, it would be very
easy: the area of the rectangle minus the area of the semicircle. But in this
case I think I have to consider that the cylinder cut the rectangular prism
with a inclination, but I am not sure.

2. Sep 17, 2008

### HallsofIvy

Staff Emeritus
Re: geometry

That's only 3 faces. I would assume the other 3 are x=0, y= 0, z= 0 but you mention x= 1 below. Are the faces x= 1, y= 0, z= 0, x= 2, y= 0.5, z= 1?

The height is not relevant if the cylinder goes all the way through the prism. But the precise location is. What line is the axis of the cylinder? "45 grads"= $0.45\pi/2$ radians.

The area of the faces is trivial. Do you mean the area of each face inside the cylinder?