Tape newspapers or kraft paper together to make an 80-inch square. Tape a string to the exact center of the square. Tie a pencil to the end of the string at exactly 80 inches. Using the string and pencil as a compass, draw an 80-inch-diameter circle on the paper. Cut out the circle with scissors.
Lay the paper circle on the floor in the bedroom. Determine if there is enough room for an 80-inch round bed plus your other furniture. If not, cut the circle down to 70 inches.
Put on gloves, safety glasses and a dust mask before working with foam, especially if you are cutting with an electric carving knife.
Place the two foam pads side by side to make a 108-by-80-inch rectangle. Glue them together by pulling the foam pads apart by a few inches and applying contact cement to the inner sides. Allow the contact cement to dry according to the manufacturer's directions, then press the two pads together firmly. Allow the contact cement to finish drying before proceeding.
Draw an 80-inch circle on top of the foam pad with your string compass and a marker. Using a sharp knife, utility knife or electric carving knife, slowly cut out the circle. To avoid a jagged line, cut through the foam using several strokes of the knife as you work your way around the circle.
Repeat the process with the egg crate foam, cutting it into an 80-inch-circle. Then cut the memory foam into an 80-inch-circle.
Layer the parts of the mattress on the bed platform with the foam pad on the bottom, then the egg crate foam and the memory foam on top. The foam will tend to stick together due to friction; ask a helper to assist you in aligning the pieces and dropping them into place. Alternate the placement of the seams so no two seams are lined up with another.
Make the bed using round sheets. Round waterbed sheets are available in 70- and 80-inch sizes. Custom sizes are available through your local seamstress and online vendors.