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2020 AMC 10A Problems/Problem 10

Revision as of 20:55, 31 January 2020 by Pcchess (talk | contribs) (Created page with "{{duplicate|2020 AMC 12A #7 and 2020 AMC 10A #10}} ==Problem 10== Seven cubes, whose volumes are <math>1</math>, <math>8<...")
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The following problem is from both the 2020 AMC 12A #7 and 2020 AMC 10A #10, so both problems redirect to this page.

Problem 10

Seven cubes, whose volumes are $1$, $8$, $27$, $64$, $125$, $216$, and $343$ cubic units, are stacked vertically to form a tower in which the volumes of the cubes decrease from bottom to top. Except for the bottom cube, the bottom face of each cube lies completely on top of the cube below it. What is the total surface area of the tower (including the bottom) in square units?

$\textbf{(A)}\ 644\qquad\textbf{(B)}\ 658\qquad\textbf{(C)}\ 664\qquad\textbf{(D)}\ 720\qquad\textbf{(E)}\ 749$

Solution

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