How do you determine the volume of regular and irregular bodies?

Answer 1

When measuring for the volume of regular solids, such as dice, it's as simple as length times width times height. The formula looks like this:

V = (l)(w)(h)

(Volume is usually measured in cubic centimeters [cm3])

When measuring for the volume of irregular solids, such as marbles, you need a graduated cylinder. Fill the graduated cylinder up to whatever number you wish (ex. 20mL).

*Make sure you remember that number*

Put the irregular substance into the cylinder (Tip: Tilt the cylinder and gently slide the object to the bottom if it's a glass cylinder) and get the reading in milliliters (mL). Now subtract the old reading by the new reading and you have the volume of the irregular object in milliliters. If you want to convert the milliliters into cubic centimeters, just remember this:

1 cubic centimeter = 1 milliliter

Answer 2

For several regular solids, there are well-known formulae - for example, for spheres, rectangular boxes, pyramids, cylinders, and others. For irregular solids, one method is to do measurements - an object can be immersed in a liquid, and the amount of liquid displaced can be measured. Another option is to split the object into small pieces in the shape of rectangular blocks or some other shape (perhaps the "splitting" is only in calculations), and add the volume of all the pieces. This is called "integration". In fact, many of the well-known formulae for regular solids - such as a sphere - have also been obtained through integration.