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Geometry and Trigonometry / Area and volume Difficulty: Hard

A right square prism has a height of $14$ units. The volume of the prism is $2,016$ cubic units. What is the length, in units, of an edge of the base?

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Explanation

The correct answer is $12$ . The volume, $V$ , of a right square prism can be calculated using the formula $V = s^{2} h$ , where $s$ represents the length of an edge of the base and $h$ represents the height of the prism. It’s given that the volume of the prism is $2,016$ cubic units and the height is $14$ units. Substituting $2,016$ for $V$ and $14$ for $h$ in the formula $V = s^{2} h$ yields $2,016 equals left parenthesis s squared right parenthesis left parenthesis 14 right parenthesis$ . Dividing both sides of this equation by $14$ yields $144 equals s squared$ . Taking the square root of both sides of this equation yields two solutions: $- 12 = s$ and $12 equals s$ . The length can't be negative, so $12 equals s$ . Therefore, the length, in units, of an edge of the base is $12$ .