Volume of a Cone and Cylinder
9 Step-by-Step Examples!

Did you know that the volume of a cone and cylinder is related?

It’s true

You’re going to learn how to use this relationship to find volumes and surface areas of both cones and cylinders in today’s geometry lesson.

Also, you’ll learn how to tackle composite figures made up of cones and cylinders.

Let’s jump in!

There are two famous three-dimensional solids: the cylinder and the cone.

A cylinder is made up of two congruent, parallel, circular bases and one lateral face the shape of a rectangle.

To calculate the volume of the cylinder, we must first find the area of the base and then multiply by the height of the cylinder.

To find the surface area of a cylinder, we use our area and circumference formulas. First, we see the area of the two parallel, circular bases, and then we calculate the area of the rectangular lateral face. The trick for finding the area of this polygon is to know that the length is actually the circumference of the circle!

Don’t worry. We walk through several step-by-step examples in the video below.

Now, a cone is a solid that resembles an ice cream cone and has only one circular base and one lateral face. Its volume is one-third that of a cylinder, and its surface area is the product of the area of the base and the lateral face, as Math is Fun accurately states.

And the method we use to find the area of the lateral surface is similar to finding the area of a triangle where the lateral edge is the hypotenuse. Again, this method is depicted in the video that follows.

Next, you’ll learn how to:

1. Calculate the volume and surface area for all different types of cylinders and cones.
2. Use the volume addition postulate to find the volume of composite solids.

Video – Lesson & Examples

58 min

• Introduction to video: cylinders and cones
• 00:00:25 – Formulas for finding the volume and surface area of a cylinder and cone
• Exclusive Content for Member’s Only

• 00:07:22 – Find the volume of the solid (Examples #1-4)
• 00:16:06 – Find the surface area of the solid (Examples #5-8)
• 00:26:27 – Find the volume and surface of the composite solid (Example #9)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions