248 views

### Area of a spherical cap crossing an intersection [duplicate]

Consider the following background information: I have a sphere that equally divided in to two hemisphere P and S. There is a plane that separate two different zone. Upper zone called A and lower zone ...
180 views

### Area of a spherical cap across an intersection [duplicate]

I have a sphere with radius $r$ that equally divided in to two hemisphere P and S. There is a plane that separate two different zone A and B. Upper zone called A and lower zone called B. $\alpha$ is ...
70 views

### calculate surface area of a spherical ball's portion [duplicate]

Imagine a spherical ball with radius r that equally coated into two hemisphere P(grey) and S(white) is thrown at the pool. Consider the ball can float (up-down) and rotate. There is an interface ...
59 views

### Calulate area when two circle intersect each other [duplicate]

I have Sphere with radius R. Inside the sphere I have Two circle. One circle is fixed defined by $\alpha$. Another circle can rotate and the orientation of that circle can be defined by $\beta$. From ...
54 views

### calculate complex geometry for a dynamic system [duplicate]

Imagine a spherical ball with radius r that equally coated into two hemisphere P(grey) and S(white) is thrown at the pool. Consider the ball can float (up-down) and rotate. There is an interface ...
I am using spherical coordinate system $r,\theta, \phi$ like this picture. Consider I have a sphere with radius $R$, is divided into two hemisphere $S$ and $P$. With this given information I am able ...