Hi guys,
I need some urgent
help with a problem of applied geometry:
There are 4 spheres. Each of them has a volume of 42 ml, which yields a radius of 2.156 cm. The distance of the 4 spheres to each other (central points) is always 1 cm. Because the radius of each sphere is larger than the 1 cm distance, the spheres are superimposing each other. The task is to calculate the total volume of all 4 spheres minus the superimposing parts, being an "effectively visible" volume of the whole 4-spheres body.
The parameter are:
r: radius of one sphere = 2.156 cm
V: volume of one sphere = 42 ml
d: distance between one central point of a sphere to the other = 1 cm
V(total): the total volume of all 4 spheres = 168 ml
V(lens): the volume of all spheres superimposing to each other
V(eff): V(total) - V(lens)
I solved the problem for two spheres using the following equation (V(total) = 84 ml):
(1) V(lens) = 1/12 x pi (4r + d)(2r - d) 2
(2) V(lens) = 0.262 * 9.624 * 10.97 = 27.66 ml
(3) V(eff) = 84 ml - 27.66 ml = 56.34 ml, i.e. V(eff) is 33% smaller than V(total).
Can anyone help me to extend the formula (1) for 4 superimposing spheres???
I need V(lens) for 4 superimposing spheres. Please.
I need some urgent
There are 4 spheres. Each of them has a volume of 42 ml, which yields a radius of 2.156 cm. The distance of the 4 spheres to each other (central points) is always 1 cm. Because the radius of each sphere is larger than the 1 cm distance, the spheres are superimposing each other. The task is to calculate the total volume of all 4 spheres minus the superimposing parts, being an "effectively visible" volume of the whole 4-spheres body.
The parameter are:
r: radius of one sphere = 2.156 cm
V: volume of one sphere = 42 ml
d: distance between one central point of a sphere to the other = 1 cm
V(total): the total volume of all 4 spheres = 168 ml
V(lens): the volume of all spheres superimposing to each other
V(eff): V(total) - V(lens)
I solved the problem for two spheres using the following equation (V(total) = 84 ml):
(1) V(lens) = 1/12 x pi (4r + d)(2r - d) 2
(2) V(lens) = 0.262 * 9.624 * 10.97 = 27.66 ml
(3) V(eff) = 84 ml - 27.66 ml = 56.34 ml, i.e. V(eff) is 33% smaller than V(total).
Can anyone help me to extend the formula (1) for 4 superimposing spheres???
I need V(lens) for 4 superimposing spheres. Please.