Using the expressions for the infinitesimal elements of length derived and discussed in § {Activity: Infinitesimal Distance in Cylindrical and Spherical Coordinates} and § {Wrap-Up: Infinitesimal Distance in Cylindrical and Spherical Coordinates}, you should find explicit formulas for the surface or volume elements in each of the following cases:

• the scalar surface elements for the three surfaces (top, bottom, and curved side) of a cylinder with finite length;
• the scalar surface element for a horizontal plane through the $z$-axis;
• the scalar surface element for the surface of a sphere.
• the volume element of a cylinder;
• the volume element for a sphere.

You may find the diagrams in § {Infinitesimal Distance in Cylindrical and Spherical Coordinates} to be helpful.