Like Brobdingnagian spools of thread, three giant steel cones in the hold of an unusual ship here are wrapped with up to 3,000 miles of cable no thicker than a garden hose. The cable, composed of six hair-thin strands of glass covered by steel and plastic, can carry 40,000 telephone calls across the ocean floor at a time.

The American Telephone and Telegraph Company, which owns the ship, hopes to lay 20,000 miles of such cable within several years. The effort is but one of many by the world's major telephone companies to keep up with international telephone traffic, which is doubling every four years and is expected to grow faster if a recently proposed United States rate-cutting effort succeeds.

The telephone companies are not only speeding up the laying of fiber-optic cables to supplement copper ones, but also making the first large round of orders for cable-laying ships in a generation. At the same time, research into better electronics is producing cables that can carry even more calls, while new techniques are providing more protection for cables against hazards ranging from shark bites to equipment used by fishing boats to harvest clams on the sea floor.

The next trans-Atlantic telephone cable, scheduled for deployment in 1992, will use sophisticated electronics to carry 80,000 lines - compared with 48 lines on the first telephone cable, laid in 1956. The latest cables are armored against shark bites with two layers of steel tape and buried deeper than before under the sea bed in shallow waters to prevent damage from fishing boats.