A manufacturer determined that right cylindrical containers with a height that is 4 inches longer than the radius offer the

Question

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?

Accepted Answer

Choice D is correct. The volume, V , of a right cylinder is given by the formula , 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 represents the height of each cylindrical container. It follows that the volume of each container is represented by the equation . Distributing the expression into each term in the parentheses yields . Choice A is incorrect and may result from representing the height as instead of . Choice B is incorrect and may result from representing the height as instead of . Choice C is incorrect and may result from representing the volume of a right cylinder as instead of .

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