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How to 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 1 inch (2.5 cm).
    • 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 inch3is really just 1 inch (2.5 cm) x 1 inch (2.5 cm) x 1 inch (2.5 cm). The result of 1 inch3is 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 2 inches (5.1 cm), 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 readV = ⁴⁄₃ x π x 1,orV = 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 asV = 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

Community Q&A

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  • Question
    Why is the formula not V = pi x R squared x H?
    Diante Watts
    Community Answer
    Height is not included when measuring spheres, since usually they are congruent in all directions; it wouldn't be a necessity, because the radius is included.
    Thanks!
  • Question
    How do I find the volume with only the circumference given?
    wikiHow Contributor
    Community Answer
    Use the circumference formula (C=2πr) and rearrange it to solve for the radius (r=C/2π). Once you have the radius (r), you can use that value in the volume of a sphere formula (V = 4/3πr³).
    Thanks!
  • Question
    What is the volume of a sphere if the radius is 6?
    Smile Happy
    Community Answer
    Use the formula V= 4/3(3.14)(6^3). 6*6*6 = 216, V= 4/3*3.14*216, V=4*3.14*216= 2,712.96, 2,712.96/3 = 904.32. So the volume would be 904.32.
    Thanks!
  • Question
    How can I tell the volume with only the diameter given?
    wikiHow Contributor
    Community Answer
    Divide the diameter by 2, giving you the radius and continue from there.
    Thanks!
  • Question
    I need to know the volume of a cylindrical water tank with ellipsoidal bases.
    wikiHow Contributor
    Community Answer
    V=pi *a*b*h where "a" and "b" are the semi-major and semi-minor axes of the ellipse, and "h" is the height of the cylinder.
    Thanks!
  • Question
    How can I calculate volume from a diameter?
    Top Answerer
    Divide by 2, then take that radius and plug it into the volume formula.
    Thanks!
  • Question
    How do I find the diameter with only the volume given?
    Top Answerer
    Use the volume formula to solve for the radius, then double the radius.
    Thanks!
  • Question
    If one sphere is 1000 times larger in diameter than another, how many times larger is its volume?
    Top Answerer
    One billion times larger.
    Thanks!
  • Question
    Between a sphere 32 mm diameter and a sphere 18 mm diameter, what is percentage difference?
    Top Answerer
    If you're asking only about the diameters, divide 18 by 32. That gives you a decimal number. Multiply it by 100 to get what percentage 18 is of 32. If you want to compare the two volumes, you'll have to cube each diameter and then perform the same division operation.
    Thanks!
  • Question
    If a sphere is placed on a flat surface, how do I calculate the actual amount of the sphere that is making contact with the flat surface?
    Top Answerer
    Theoretically there is only a point (and not an "area") that contacts the flat surface. In practice, there is no formula for finding the area that actually touches the surface.
    Thanks!
Unanswered Questions
  • How do I calculate the cubed inches of a sphere if the radius is a decimal?
  • How do I calculate the volume of a flat sand bag?
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Quick Summary

To calculate the volume of a sphere, use the formula v = ⁴⁄₃πr³, where r is the radius of the sphere. If you don't have the radius, you can find it by dividing the diameter by 2. Once you have the radius, plug it into the formula and solve to find the volume.

Did this summary help you?
  • 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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Date: 12.01.2019, 22:33 / Views: 73592