Our cylinder volume calculator enables calculating the volume of that solid. Whether you want to figure how much water fits in the can, coffee in your favorite mug, or even what's the volume of a drinking straw - you're in the right place. The other option is calculating the volume of a cylindrical shell hollow cylinder. Let's start from the beginning - what is a cylinder? It's a solid bounded by a cylindrical surface and two parallel planes.

## Shell method

## Volumes by Cylindrical Shells - Mathematics LibreTexts

In this section, we examine the method of cylindrical shells, the final method for finding the volume of a solid of revolution. We can use this method on the same kinds of solids as the disk method or the washer method; however, with the disk and washer methods, we integrate along the coordinate axis parallel to the axis of revolution. With the method of cylindrical shells, we integrate along the coordinate axis perpendicular to the axis of revolution. The ability to choose which variable of integration we want to use can be a significant advantage with more complicated functions. Also, the specific geometry of the solid sometimes makes the method of using cylindrical shells more appealing than using the washer method.

### 6.3: Volumes by Cylindrical Shells

In this section, we examine the method of cylindrical shells, the final method for finding the volume of a solid of revolution. We can use this method on the same kinds of solids as the disk method or the washer method; however, with the disk and washer methods, we integrate along the coordinate axis parallel to the axis of revolution. With the method of cylindrical shells, we integrate along the coordinate axis perpendicular to the axis of revolution.

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