The sphereflake shown (not shown for question) is a computergenerated 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 . Attached to each of the smaller spheres are nine spheres of radius . This process is continued infinitely.

Question

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.) Determine if either the surface area or the volume of the sphereflake is finite or infinite. If either is finite, find the value.

Answer 1

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Answer 2

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