Calculate the Volume of a Sphere

A sphere is a perfectly round geometrical object that is three dimensional, with every point on its surface equidistant from its center. Many commonly-used objects such as balls or globes are spheres. If you want to calculate the volume of a sphere, you just have to find its radius and plug it into a simple formula, V = ⁴⁄₃πr³.

Steps

  1. Write down the equation for calculating the volume of a sphere. This is the equation: V = ⁴⁄₃πr³. In this equation, "V" represents volume and "r" represents the radius of the sphere.
  2. Find the radius. If you're given the radius, then you can move on to the next step. If you're given the diameter, then you can just divide it by two to get the radius. Once you know what it is, write it down. Let's say the radius we're working with is {{safesubst:#invoke:convert|convert}}.[1]
    • If you're only given the surface area of the sphere, then you can find the radius by finding the square root of the surface area divided by 4π. In that case, r = root (surface area/4π)
  3. Cube the radius. To cube the radius, simply multiply it by itself thrice, or raise it to the third power. For example, 1 inch3 is really just {{safesubst:#invoke:convert|convert}} x {{safesubst:#invoke:convert|convert}} x {{safesubst:#invoke:convert|convert}}. The result of 1 inch3 is really just 1, since 1 multiplied by itself any number of times will be 1. You'll reintroduce the unit of measurement, inches, when you state your final answer. After you've done this, you can plug the cubed radius into the original equation for calculating the volume of a sphere, V = ⁴⁄₃πr³. Therefore, V = ⁴⁄₃π x 1
    • If the radius was {{safesubst:#invoke:convert|convert}}, for example, then to cube it, you would find 23, which is 2 x 2 x 2, or 8.
  4. Multiply the cubed radius by 4/3. Now that you've plugged r3, or 1, into the equation, you can multiply this result by 4/3 to continue plugging in to the equation, V = ⁴⁄₃πr³. 4/3 x 1 = 4/3. Now, the equation will read V = ⁴⁄₃ x π x 1, or V = ⁴⁄₃π.
  5. Multiply the equation by π. This is the last step to finding the volume of a sphere. You can leave π as it is, stating the final answer as V = ⁴⁄₃π. Or, you can plug π into your calculator and multiply its value by 4/3. The value of π (approximately 3.14159) x 4/3 = 4.1887, which can be rounded to 4.19. Don't forget to state your units of measurement and to state the result in cubic units. The volume of a sphere with the radius of 1 is 4.19 in.3



Tips

  • Don't forget to use cubed units (e.g. 31 ft³ ).
  • Make sure your measurements are all in the same unit. If they aren't, you will need to convert them.
  • Note that the "*" symbol is used as a multiplication sign to avoid confusion with the variable "x".
  • If you only need part of a sphere, like half or a quarter, find the full volume first, then multiply by the fraction you want to find. For instance, to find the volume of half a sphere with a volume 8, you would multiply 8 by one half or divide 8 by 2 to get 4.

Things You'll Need

  • Calculator (reason: to calculate problems that would be annoying to do without it)
  • Pencil and paper (not needed if you have an advanced calculator)

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Sources and Citations

  1. ↑ http://www.teacherschoice.com.au/maths_library/area%20and%20sa/area_2.htm
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