posted by .

Why do you use 1/3 in volume formulas?

  • geometry -

    any solid that comes to a vertex or point has the formula
    V = (1/3) (base area) x (height)

    I you know Calculus you could take the region bounded by the x-axis, the y-axis and a line with x-intercept of h and y-intercept of r and rotate it about the x-axis

    The result will be a cone with radius r and height h
    the equation of that line is
    y = (-r/h)x + r

    the generated volume
    = π[integral]y^2 dx
    = π[integral] (r^2x^2/h^2 - 2r^2x/h + r^2) dx
    = π [r^2x^3/(3h^2) - r^2x^2/h + r^2x] from 0 to h
    = π(r^2h/3 - r^2h + r^2h - 0)
    = π(r^2)(h)/3
    = (1/3)(πr^2)(h) or (1/3)basearea x height

    When I was still teaching, I had a cylinder and a cone, both with the same radius and height.

    In class we would fill the cone with water and pour it into the cylinder, and do that until the cylinder was full.
    We were able to fill and pour THREE times, showing that the volume of the cone was
    (1/3) of the volume of the cylinder.

    volume of cylinder = πr^2h
    volume of cone = (1/3)πr^2h

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    Okay. So i'm doing this project for my geometry class about different sports, soccer, baseball, basketball, bowling, golf, volleyball and pool. I have to find the surface area, volume, diameter, circumference, and radius of each of …
  2. Math

    When something says that I'll be tested on formulas for perimeter and area of polygons, does that mean I'll just have to know the formulas, or that I'll have to know how to use the formulas, or both?
  3. Statistics

    Hi, My professor gave us the formulas for sample variance and population variance, as well as the shortcut formulas for each. However, he said that on some of the problems, we will HAVE to use the long formula, which for population …
  4. geometry

    Looking at formulas, which 2 shapes describe this relationship: the area of the 2 dimensional shape is one-fourth the surface area of the 3-demensional figure?
  5. math

    Can you describe some common formulas that you use in your life?
  6. geometry

    A hemispherical dome holds a volume of 486π..find the surface area (omit the area of the circle)?
  7. computer applications

    John wants to see the formulas he has used in his spreadsheet but he does not want to see the results of the formulas. How does he display his formulas?
  8. Geo

    Hi I need some major help on surface area and volume. Do you think you can provide some examples for me to solve out?
  9. Intro to computers

    You are an inexperienced Excel user and don’t know how to create your own formulas. You want to use one of the preconfigured formulas but it doesn’t appear in the Formulas tab ribbon. What can you do?
  10. Math- Formulas

    What are some formulas that you use in everyday life and how do you use them?

More Similar Questions