I would first find the volume of the two cones on the end and add them to the volume of the cylinder in the center. Then, subtract these from the the volume of a sphere with a 14 ft radius, which is the length of the line.
A submersible tank is stationary in deep sea water.
It has right cone shaped ends 6ft. in diameter and 4ft. in length and a
cylindrical centre section which is 6ft. in diameter and 4ft. in length.
The overall length therefore is 12ft.
i.e. like this < >
A diver is attached externally to one cone apex by a 14ft. lifeline which
just gives him access to the other cone apex.
What volume of sea water does he have access to?
I can't get what is given as answer: approx 11,240.5 cubic feet.
Oh... I see, the rope gets shorter as he gets nearer the opposite end, where the radius at the end is 12 feet and the radius out into the ocean is 14. Could you solve it by taking a few "slices" of the sphere? by taking the slice where the radius is a ceartain amount, then another where the radius is the next size, and so on until it has no contact with the tank and is 14 feet?
Math Forum - Ask Dr. Math
Could this help? also, is it posible this problem could need any calclus?