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Yes, It is round, but the part of the speaker that vibrates forward and backwards is called the cone; if looked at sideways, it is cone-shaped. This cone is allowed to vibrate because it is suspended by a rubber or foam or paper perimeter, called the "front suspension surround." Unfortunately, when you have speakers for this length of time, and it often can happen sooner, the surround starts to deteriorate, often drying out and breaking apart. In addition, just the use of the speaker for that period of time, would cause normal wear on the surround. It is not worth trying to fix these speakers themselves. Your best bet is to remove just the speakers that are not good anymore, out of the speaker box, and simply replace them with new speakers that are the same size. This way you are not replacing the entire speaker cabinet/ tweeters, etc. The speaker is usually just screwed in to the cabinet from the outside, under the fabric. A foam tape is often between the speaker and the cabinet to make it airtight.....you may want to replace this when putting in the new speaker. And lastly the speaker usually has two plug wires that you would simply unplug from the old and plug into the new.
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Best of Luck, Brian
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Here is a cross-section thru a speaker.
I have built my own speaker boxes plenty of times, and I have also replaced worn out speakers, just like the situation you are in. It is very easy to do, if you want to do it yourself......then it would just be the cost of new speakers, which have a high range in prices. I would just get something in the mid-range price. You could research EBAY or your local audio store.
Click here to see how easy it is to replace a speaker.
If you are not comfortable replacing them, then you would have to bring them to an audio store. Some repairers may even come to you.....it would be worth researching, since you say they are heavy. I do not know what the labor cost would be, because I have only repaired my own, but it shouldn't be that much since I can replace one in about 5 minutes.