Question 945165
the cylinder has a diameter of 4.67 meters.
this means it has a radius of 3.335 meters.
when the diving bell is immersed in the tank, the water level goes up 1 meter.
the volume of water displaced is therefore equal to the volume of a cylinder that has a diameter of 4.67 meters and a height of 1 meter.
the volume would be equal to pi * r^2 * h which is equal to pi * 3.335^2 which is equal to 3.335^2 * pi.


the volume of a sphere is equal to 4/3 * pi * r^3.
the radius of the sphere is not the same radius as the cylinder, however.
the radius of the sphere is what we need to solve for.
that sphere must have the same volume as the water that was displaced which is equal to pi * 3.335^2.


your equation becomes:
volume of sphere is equal to the volume of the 1 meter high section of the cylinder.
you get:
volume of sphere = 4/3 * pi * r^3 which is equal to the volume of the 1 inch high section of the cylinder which is equal to 3.335^2 * pi.
the equation without all the words is":
4/3 * pi * r^3 = 3.335^2 * pi.


multiply both sides of this equation by 3/4 and divide both sides of this equation by pi to get r^3 = 3/4 * 3.335^2 * pi / pi.
simplify to get r^3 = 8.34166875.
solve for r to get r = 2.028076409.


the radius of the sphere is equal to 2.028076409.
the volume of the sphere is equal to 4/3 * pi * 2.028076409^3 which is equal to 11.122225 * pi.
the volume of the 1 inch high section of the cylinder is equal to 3.335^2 * pi which is equal to 11.122225 * pi.


the volume of the sphere is the same as the volume of the 1 meter high section of the cylinder.
the diameter of the diving bell is the same as the diameter of the sphere (they are the same thing) which is 2 times the radius of the sphere which makes the diameter of the diving bell equal to 4.056152818 meters which is equal to 4.06 meters rounded to 2 decimal places.