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Geometry and Trigonometry Difficulty: Hard

A manufacturer determined that right cylindrical containers with a height that is 4 inches longer than the radius offer the optimal number of containers to be displayed on a shelf. Which of the following expresses the volume, V, in cubic inches, of such containers, where r is the radius, in inches?

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Explanation

Choice D is correct. The volume, V, of a right cylinder is given by the formula $V equals, pi r squared, times h$ , where r represents the radius of the base of the cylinder and h represents the height. Since the height is 4 inches longer than the radius, the expression $r plus 4$ represents the height of each cylindrical container. It follows that the volume of each container is represented by the equation $V equals, pi r squared times, open parenthesis, r plus 4, close parenthesis$ . Distributing the expression $pi r squared$ into each term in the parentheses yields $V equals, pi r cubed, plus 4 pi r squared$ .

Choice A is incorrect and may result from representing the height as $4 r$ instead of $r plus 4$ . Choice B is incorrect and may result from representing the height as $2 r$ instead of $r plus 4$ . Choice C is incorrect and may result from representing the volume of a right cylinder as $V equals pi r h$ instead of $V equals, pi r squared, times h$ .