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Geometry and Trigonometry Difficulty: Medium

The length of the edge of the base of a right square prism is $6$ units. The volume of the prism is $2,880$ cubic units. What is the height, in units, of the prism?

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Explanation

Choice D is correct. The volume, $V$ , of a right square prism is given by the formula $V = s^{2} h$ , where $s$ represents the length of the edge of the base and $h$ represents the height of the prism. It’s given that the volume of a right square prism is $2,880$ cubic units and the length of the edge of the base is $6$ units. Substituting $2,880$ for $V$ and $6$ for $s$ in the formula $V = s^{2} h$ yields $2,880 equals left parenthesis 6 squared right parenthesis h$ , or $2,880 equals 36 h$ . Dividing both sides of this equation by $36$ yields $80 equals h$ . Therefore, the height, in units, of the prism is $80$ .

Choice A is incorrect. This is the height, in units, of a right square prism where the length of the edge of the base is $6$ units and the volume of the prism is $144 StartRoot 30 EndRoot$ , not $2,880$ , units.

Choice B is incorrect. This is the area, in square units, of the base, not the height, in units, of the prism.

Choice C is incorrect. This is the height, in units, of a right square prism where the length of the edge of the base is $6$ units and the volume of the prism is $864 StartRoot 5 EndRoot$ , not $2,880$ , units.