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A scale, a beaker and a graduated cylinder. You use the scale to determine the mass of the object. If it is a solid, you can just place it on the scale. If it is a liquid you have to keep it in a graduated cylinder or beaker and weigh it. But remember to subtract the weight of the beaker/graduated cylinder.

Then you have to find the volume. For a liquid, this is very easy. Just put it into a graduated cylinder and read the ml on the side. If it's a solid, then there are two ways to do it. If it is a very even shape, such as a cube or a cylinder etc, you can take precise measurements and use the volume equations available for the certain shape. Another way is to do water displacement. Put water into the beaker and record the volume. Then put the solid in the water (make sure the solid doesn't dissolve in water first). Record the volume and subtract the original volume.

The density is just mass divided by volume.

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