In a cube of side "a", a sphere with center in one of the vertices intersects another sphere located in the vertex opposite to the previous one. What is the volume of the intersection?
First I tried to draw the situation The equation of one of the spheres centered at the origin is
$$x^2+y^2+z^2 =a^2$$ And the one located on the opposite vertex will be
2 questions How to plot the situation? How to calculate the common volume?
I used several commands but I did not get the cube and the 2 spheres at the same time in a drawing
Thanks in advance
Edited: There was an error in the radios of the spheres, they have radius "a", similar to the edges of the cube