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Geometry and Trigonometry / Area and volume Difficulty: Hard

A cube has a volume of $474,552$ cubic units. What is the surface area, in square units, of the cube?

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Explanation

The correct answer is $36,504$ . The volume of a cube can be found using the formula $V = s^{3}$ , where $s$ represents the edge length of a cube. It’s given that this cube has a volume of $474,552$ cubic units. Substituting $474,552$ for $V$ in $V = s^{3}$ yields $474,552 equals s cubed$ . Taking the cube root of both sides of this equation yields $78 equals s$ . Thus, the edge length of the cube is $78$ units. Since each face of a cube is a square, it follows that each face has an edge length of $78$ units. The area of a square can be found using the formula $A = s^{2}$ . Substituting $78$ for $s$ in this formula yields $upper A equals 78 squared$ , or $upper A equals 6,084$ . Therefore, the area of one face of this cube is $6,084$ square units. Since a cube has $6$ faces, the surface area, in square units, of this cube is $6 left parenthesis 6,084 right parenthesis$ , or $36,504$ .