In a fractal, a geometric figure is repeated at smaller and smaller scales. The
Chapter 9, Problem 109(choose chapter or problem)
In a fractal, a geometric figure is repeated at smaller and smaller scales. The sphereflake shown is a computer-generated fractal that was created by Eric Haines. The radius of the large sphere is 1. Attached to the large sphere are nine spheres of radius \(\frac{1}{3}\). Attached to each of the smaller spheres are nine spheres of radius \(\frac{1}{9}\). This process is continued infinitely.
(a) Write a formula in series notation that gives the surface area of the sphereflake.
(b) Write a formula in series notation that gives the volume of the sphereflake.
(c) Is the surface area of the sphereflake finite or infinite? Is the volume finite or infinite? If either is finite, find the value.
Text Transcription:
1/3
1/9
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