Volumes by Cylindrical Shells2

Front

WHAT IS THE RADIUS OF A CYLINDRICAL SHELL?

Back

Front

HOW DO YOU DETERMINE THE HEIGHT OF A CYLINDRICAL SHELL?

Back

The height of a cylindrical shell is determined by the difference between the upper and lower functions that define the region being revolved.

Front

WHAT IS THE FORMULA FOR THE VOLUME OF A CYLINDRICAL SHELL?

Back

Front

WHAT DOES THE INTEGRAL LIMITS REPRESENT IN VOLUME CALCULATIONS?

Back

The integral limits represent the bounds of the region being revolved around the axis, typically the x-values where the region starts and ends.

Front

HOW DOES THE RADIUS CHANGE WITH RESPECT TO X?

Back

Front

WHAT IS THE SIGNIFICANCE OF THE AXIS OF ROTATION?

Back

The axis of rotation is the line around which the region is revolved to create the cylindrical shell, affecting the radius and volume calculations.

Front

HOW DO YOU SET UP AN INTEGRAL FOR VOLUME USING CYLINDRICAL SHELLS?

Back

To set up an integral for volume using cylindrical shells, identify the radius and height functions, then integrate the product of these functions multiplied by 2π over the interval.

Front

WHAT IS THE DIFFERENCE BETWEEN DISK AND SHELL METHODS?

Back

The disk method slices the solid perpendicular to the axis of rotation, while the shell method slices parallel to the axis, using cylindrical shells.

Front

GIVE AN EXAMPLE OF A FUNCTION USED IN SHELL METHOD VOLUME CALCULATIONS.

Back

Front

WHAT IS THE ROLE OF THE FUNCTION IN DETERMINING HEIGHT?

Back

The function defines the height of the cylindrical shell, which is the vertical distance between the upper and lower curves.