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Exercise 24

Avg difficulty 2.5

In this exercise, we explore how to use a parametrization and iterated integral to determine the surface area of a sphere.

  1. Set up an iterated integral whose value is the portion of the surface area of a sphere of radius RR that lies in the first octant (see the parameterization you developed in Activity).

  2. Then, evaluate the integral to calculate the surface area of this portion of the sphere.

  3. By what constant must you multiply the value determined in (b) in order to find the total surface area of the entire sphere.

  4. Finally, compare your result to the standard formula for the surface area of sphere.

Long, Keller & Schlicker, Active Calculus Multivariable, §13.10 Parameterizations of Surfaces and Surface Area, Exercise 24

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Adapted from Active Calculus Multivariable © 2013–2026 Nicholas Long, Mitchel T. Keller, and Steven Schlicker. Licensed under CC BY-SA 4.0. Source: Active Calculus Multivariable. Imported at revision 692c03c.