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Lesson 87: Volume Formulas
You've already learned how to compute the volume of a rectangular solid. Now we'll learn how to do the same for other three-dimensional objects.
This lesson just involves some memorizing of formulas. If you are absolutely certain that these formulas will be provided to you on a test, then memorizing them is not as critical, but it is essential that you understand how to use them, and how and why they work.
Recall that the formula for the volume of a rectangular prism (e.g. a shoebox) is given by V = lwh. We just multiply the three dimensions. Remember that the answer is always given in cubic units (unit3).
The volume of a cylinder (e.g. a tube) is V = πr2h. The πr2 is the area of one of the circular ends, and then we must multiply that by the height (or length), to find the volume.
The volume of a cone (like an ice cream cone) is V = (1/3)πr2h. It turns out that if you take a cylinder, and sculpt it into a cone, the cone is exactly one-third the volume of the original cylinder from which is was fashioned.
The volume of a pyramid is V = (1/3)Bh. Here, we're using B to mean the area of the base of the pyramid. That's why we use a capital B. If we're given that area, then we're all set to use it in the formula. If we are just told the dimensions of the base, then we first have to calculate the area, and then that will be the value of B that we'll use in the formula.
The volume of a sphere (e.g. a globe or ball) is V = (4/3)πr3
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