How to Find the Volume of a Sphere

What’s a sphere, exactly? 

A sphere is a 3D object based on a circle. Spheres are everywhere in our daily lives. From raindrops to planets, sports balls to chocolate bonbons. Figuring out the volume of a sphere formula and its surface area has many important real-life applications.

In this article, you’ll learn how to find the volume and surface area of a sphere using its radius r.

Important mathematical vocabulary:

• Sphere — A solid, round shape where every point on the surface is the same distance from the center.
• Dimensions — A term of measurement to help define an object’s parameters.
  • An object with 0 dimensions is a dot.
  • An object with 1 dimension is a line.
  • Objects with 2 dimensions (a two-dimensional shape) are measured by height and length. Examples include squares, triangles, and circles.
  • Objects with 3 dimensions (a three-dimensional shape) are measured by height, length, and depth. Examples include cubes, triangular prisms, and spheres.
• Radius — The line that starts at the center of a circle and stops at the edge of a circle
• Diameter — A straight line that crosses a circle at its radius
• Surface area – the outer shell of a three-dimensional object
• Volume v — The amount of space a three-dimensional object can contain inside the surface area
• Pi π — A symbol that represents the perimeter of a circle divided by the diameter of a circle, which will always equal 3.14 (to two decimal places)
• Cubic units — The units used to measure volume. They are always cubed – e.g. cubic centimeters and cubic meters (or cubic inches and cubic feet)

How to find the volume of a sphere

To find the volume of the sphere, the equation is V = 4/3 πr (or pi r)³, where r is the radius of the sphere. This graphic shows a great example of a sphere’s radius. Sometimes, you might be given a sphere’s diameter in a math problem. Remember – the diameter of a sphere is twice the distance of the radius. That means you can divide the length of the diameter in half to find out the radius. 

For example, let’s say we wanted to find the total volume of a spherical chocolate candy with a radius of 2cm — this is how we’d use the volume formula:

V = 4/3 πr³

V = 4/3 (π x 2)³

Final answer = V = 33.51cm³

You can also use a sphere calculator like this one.

How to find the surface area of a sphere

To find the surface area of the sphere, we will use the formula  SA = 4πr². We’ll also go back to the chocolate candy example we used to find the volume, where the radius was 2cm.  Here is how solving for the surface area would work with the formula:

SA = 4πr²

SA = 4 x(π x 2)²

Final answer = SA = 50.27cm²

Real-life applications for volume of a sphere

Knowing how to calculate the volume of a sphere is important, and not just for success inside a mathematics classroom. Volume of a sphere has many real life applications that are spread across a wide range of areas.

In cooking, understanding the volume of a sphere as well as a generic base of knowledge for spatial relations helps when preparing round-shaped dishes, such as cakes, cookies, meatballs, etc. It also aids in the measurement of ingredients for food preparation.  

When designing submarines, ships, and other watercraft items, knowing how to calculate the volume of a sphere helps with determining the buoyancy of the items. This is a critical component of physics and engineering with sound design.

For packaging and manufacturing, designers use the calculations from determining the volume of a sphere to assist in knowing the size and capacity for various containers to efficiently and attractively pack up and display spherically shaped objects such as ball bearings, sports balls, medicine capsules, etc.

These are just a few of the many real-life applications that are affected by knowing how to calculate the volume of a sphere. What other ways can you think of that we can find a connection between the volume of a sphere and real-life?

See our sphere math worksheets here in the Kami Library.