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Australian AMC 2011 - Senior Question 19

AMC AUSTRALIA · Australian AMC 2011 - Senior

Question 19

The centre of a sphere of radius 1 is one of the vertices of a cube of side 1.

Question illustration

What is the volume of the combined solid?
  1. $\frac{7\pi}{6}+1$
  2. $\frac{7\pi}{6}+\frac56$
  3. $\frac{7\pi}{6}+\frac43$
  4. $\frac{7\pi}{8}+1$
  5. $\pi+1$