Volume and Surface Area of a Sphere
7 Examples!

What’s the key to finding the volume and surface area of a sphere?

It’s the radius!

Stay tuned to this geometry lesson, as you’ll learn all about spheres, hemispheres, and composite functions.

Let’s go!

A sphere is perfectly round and perfectly symmetrical and is the set of all points in space at a given distance (i.e., radius) from a fixed point called the center.

What is important to note is that a sphere is not a polyhedron and therefore does not have any vertices, edges, or faces.

But a sphere does have a surface and volume, and all we need to know to calculate the volume and surface area of a sphere is the measure of its radius!

Now, just like with a circle, we can divide a sphere in half. Half a sphere is called a hemisphere, and it has precisely one-half the volume of the entire sphere.

The surface area of a hemisphere is also half the surface area of the entire sphere; however, we mustn’t forget to add the area of the circular base.

Additionally, did you know anytime we slice a sphere in half, the cross-sections are all similar circles?

And, as Math Bits Notebook accurately states, a great circle is the largest circle that can be drawn on a sphere. This means that the circumference of a great circle is equal to the circumference of the circular base of a hemisphere.

Next, you’re going to learn how to:

1. Calculate the volume and surface area of a sphere using our formulas.
2. Find the surface area and volume of composite figures such as cylinders and spheres or cones and spheres.

Video – Lesson & Examples

58 min

• Introduction to spheres
• 00:00:22 – How to find the volume and surface area of a sphere (Examples #1-3)
• Exclusive Content for Member’s Only

• 00:11:33 – Find the volume and surface area of the hemisphere and composite solid (Examples #4-5)
• 00:27:27 – Find the volume and surface area of the composite solid involving spheres, cones, and cylinders (Examples #6-7)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions