MATH COUNTS QUESTION #10

Algebra Level 2

Let q be the sum of the lengths of all 12 edges of a cube, and let A be the total surface area of the cube. If q x A is k times the volume of the cube, what is the value of K?


The answer is 72.

Eric Zhu by Eric Zhu , 15, USA

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1 solution

Tom Engelsman
Nov 5, 2018

If x x be the edge length of the cube, then q = 12 x q = 12x and A = 6 x 2 A = 6x^2 . If q ⋅ A = k ⋅ x 3 q \cdot A = k \cdot x^3 , then 72 x 3 = k ⋅ x 3 ⇒ k = 72 . 72x^3 = k \cdot x^3 \Rightarrow \boxed{k = 72}.

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