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

[germana2006]

Homework Statement

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.

Homework Equations

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.

 

[HallsofIvy]

Homework Statement

Considering a rectangular prism bounded by six rectangular faces (x=2, y=0.5,
z=1)

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?

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.

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.

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

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

I need not the numerically solutions but
the analytically solution.

Homework Equations

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.