A sphere is a perfectly round three-dimensional geometric body, in which all points on the surface are equidistant from the center. Many commonly used objects, such as balloons or globes are spheres. If you want to calculate the volume you just have to find the radius and insert it in the simple formula: V = ⁴⁄₃πr³.
Steps
Step 1. Write the equation to calculate the volume of the sphere
This is: V = ⁴⁄₃πr³, where "V" represents the volume and "r" the radius of the sphere.
Step 2. Find the radius
If the problem gives you this information, then you can move on to the next step. If you are given the diameter, just divide it by two and find the radius. Once you know its value, write it down. Suppose that the radius of the sphere under consideration is 2.5 cm.
If the problem provides only the area of the sphere, then you can find the radius by extracting the square root of the surface and dividing the result by 4π. In this case r = √ (area / 4π)
Step 3. Cubic radius
To do this, simply multiply the radius by itself by three times, in other words raise it to the power of three. For example (2, 5 cm)3 equals 2.5cm x 2.5cm x 2.5cm. The result, in this case, is 15, 625 cm3. Remember that you must also express the units of measurement, centimeters, correctly: cubic centimeters are used for the volume. Once you have calculated the radius to the power of three, you can enter the value in the original equation to find the volume of the sphere: V = ⁴⁄₃πr³. Therefore V = ⁴⁄₃π x 15.625.
If the radius had been 5 cm, for example, then your cube would have been 53, i.e. 5 x 5 x 5 = 125 cm3.
Step 4. Multiply the cube of the radius by 4/3
Now that you have entered the value of r in the equation3, that is 15, 625, you can multiply it by 4/3 and continue the development of the formula: V = ⁴⁄₃πr³. 4/3 x 15, 625 = 20, 833. At this point the equation will look like this: V = 20.833 x π that is V = 20.833π.
Step 5. Perform the last multiplication by π
This is the last step to find the volume of the sphere. You can leave π as it is, stating as the final solution that V = 20.833π or you can enter the value of π into the calculator and multiply it by 20, 833. The value of π (rounded to 3, 141) x 20, 833 = 65, 4364 which you can round to 65, 44. Don't forget to also express units of measurement correctly, that is, in cubic units. The volume of a sphere with a radius of 2.5 cm is 65.44 cm3.
Advice
- Remember that the "*" symbol is used as a multiplication sign to avoid confusion with the "x" variable.
- Verify that all data are expressed with the same unit of measurement. If not, convert them.
- If you need to find only a part of the volume of the sphere, such as a quarter or half, then first calculate the entire volume and then multiply the value by the fraction you are interested in. For example, to find half the volume of a sphere with a total volume of 8, multiply 8 by ½ or divide 8 by 2 and you will get 4.
- Don't forget to express the result in cubic units (for example 31 cm3).
