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2009 AMC 10B Question 22

AMC10 · 2009 AMC 10B

Question 22

A cubical cake with edge length $2$ inches is iced on the sides and the top. It is cut vertically into three pieces as shown in this top view, where $M$ is the midpoint of a top edge. The piece whose top is triangle $B$ contains $c$ cubic inches of cake and $s$ square inches of icing. What is $c+s?$

Question illustration
  1. $\dfrac{24}{5}$
  2. $\dfrac{32}{5}$
  3. $8+\sqrt5$
  4. $5+\dfrac{16\sqrt5}{5}$
  5. $10+5\sqrt5$