Let’s learn how to determine the volume of a sphere.
What is a Sphere?
A sphere is a perfectly symmetrical three-dimensional shape whose all surface points are equidistant from the center. The distance from the center to any point on the surface is called the radius. Twice the radius is the diameter or the line segment that passes through the center. Examples of sphere-shaped objects are marbles, bubbles, and balls.
How to find the Volume of a Sphere
The volume of a sphere is four-thirds of the product of pi and radius cubed, as expressed in this formula:
V = (4/3)Ï€r3
where π = 3.14 and r = radius
Like other three-dimensional shapes, the volume of a sphere is measured in cubic units such as cubic inch (in3), cubic feet (ft3), cubic centimeter (cm3), or cubic meter (m3).
Here’s a quick guide to finding a sphere’s volume:
Step 1. Write down the given figures. You’ll need the radius or the diameter. Make sure all measurement units are the same. If not, convert either of them.
Step 2. Plug the figures into the formula.
Step 3. Perform the operations: multiplication and division. Don’t forget to write the cubit unit together with the answer.
Related Reading: Volume of a Cylinder – Formula & Examples
Example 1: Finding the Volume of a Sphere when given the Radius
Find the volume of the sphere below.
Solution for Example 1:
Write down the given figure, which is the radius (r = 3cm).
Substitute 3cm for r into the formula.
V=(4/3)Ï€r3
V=(4/3)Ï€(3cm)3
Simplify.
V=(4/3)Ï€(27cm3)
V=113.09cm3…
Therefore, the volume is about 113.09cm3.
Example 2: Finding the Volume of a Sphere when given the Diameter
Find the volume of the sphere below.
Solution for Example 2:
Write down the given figure, which is the diameter (d = 9cm). Since a sphere’s volume formula requires the value of the radius, find the radius.
You may recall that diameter is twice the radius. So, divide the diameter (d = 9cm) by 2 to obtain the radius.
r = d/2 = 9cm/2 = 4.5cm
Substitute 4.5cm for r in the equation.
V=(4/3)Ï€r3
V=(4/3)Ï€(4.5cm)3
Simplify.
V=(4/3)Ï€(91.125cm3)
V = 381.70cm3…
Therefore, the volume is about 381.70cm3.
Thank you for reading. We hope it’s effective! Always feel free to revisit this page if you ever have any questions about the volume of a sphere.
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