By integration - you divide the figure into many thin slices, and calculate the volume of each slice individually. The volume of each slice, again, can be calculated by integration: divide it into thin rectangles, and calculate the area of each rectangle.
If you have a irregular solid figure just immerse it in water and measure the displacement. a la Archimedes
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you cut it into regular solids then figure out those then add them together
The water displacement method is typically used to find the volume of an irregular solid. The object is submerged in a known amount of water, and the increase in water volume is measured. This increase in volume is equal to the volume of the irregular solid.
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To find the volume of an irregular solid using the overflow can method, you would first fill the overflow can with water and measure the initial volume. Next, you would submerge the irregular solid in the overflow can, causing the water to overflow. Measure the new volume of water in the overflow can with the solid submerged. Finally, you would subtract the initial volume from the final volume to find the volume of the irregular solid.
A graduated cylinder.