Volume and surface area

This course is a part of Geometry (all content), a 17-course Topic series from Khan Academy.

Volume and surface area help us measure the size of 3D objects. We’ll start with the volume and surface area of rectangular prisms. From there, we’ll tackle trickier objects, such as cones and spheres.

This course contains 9 segments:

Volume of rectangular prisms

Welcome to the 3rd dimension! [cue spooky music] This tutorial explains how to find volume.

Volume with fractions

Finding the volume of rectangular prisms that have fractional side lengths

Surface area

Learn how to find the total area of the surfaces of 3D shapes. To do this, we wrap 3D shapes in 2D nets.

Volume of cones, cylinders, and spheres

Let's see how to find the volumes of cylinders, spheres and other three dimensional shapes.

Solid geometry

Tired of perimeter and area and now want to measure 3-D space-take-upness. Well you've found the right tutorial. Enjoy!

Surface and volume density

Use your knowledge of surface area and volume to solve problems involving density.

Cross sections of 3D objects

It's pretty difficult to work, mentally, with 3D objects. One way of overcoming that difficulty is in thinking about cross sections of such objects. These are 2D slices of 3D objects, and so we're back with the familiar 2D world.

Koch snowflake fractal

Named after Helge von Koch, the Koch snowflake is one of the first fractals to be discovered. It is created by adding smaller and smaller equilateral bumps to an existing equilateral triangle. Quite amazingly, it produces a figure of infinite perimeter and finite area!

Heron's formula

Named after Heron of Alexandria, Heron's formula is a power (but often overlooked) method for finding the area of ANY triangle. In this tutorial we will explain how to use it and then prove it!