Calculus is a mathematical technique: it is not a unit or tool for measurement.
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It is necessary because measuring tools help you measure the length of an object accurately.
Calculus will work, if you have an equation describing the precise shape of the object. If you don't (and probably even if you do), it's far easier to actually measure it (by submerging it in water and measuring the amount of water displaced) than it is to calculate it.
It all depends on the objects.
You can use a line graph if your measuring the motion in separate experiments or comparing.
Experimentally, by filling the object with water and measuring the amount of water it takes to fill it. Solving the volume with math requires calculus, or finding the volume of parts of the shape and adding them together.