A right rectangular prism has a height of 9 inches. The length of the prism’s base is x inches, which is 7 inches more than the width of the prism’s base. Which function V gives the volume of the prism, in cubic inches, in terms of the length of the prism’s base?

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Accepted Answer

Choice D is correct. The volume of a right rectangular prism can be represented by a function V that gives the volume of the prism, in cubic inches, in terms of the length of the prism’s base. The volume of a right rectangular prism is equal to the area of its base times its height. It’s given that the length of the prism’s base is x inches, which is 7 inches more than the width of the prism’s base. This means that the width of the prism’s base is x − 7 inches. It follows that the area of the prism’s base, in square inches, is x(x − 7) and the volume, in cubic inches, of the prism is x(x − 7)(9). Thus, the function V that gives the volume of this right rectangular prism, in cubic inches, in terms of the length of the prism’s base, x, is V(x) = 9x(x − 7). Choice A is incorrect. This function would give the volume of the prism if the height were 9 inches more than the length of its base and the width of the base were 7 inches more than its length. Choice B is incorrect. This function would give the volume of the prism if the height were 9 inches more than the length of its base. Choice C is incorrect. This function would give the volume of the prism if the width of the base were 7 inches more than its length, rather than the length of the base being 7 inches more than its width.

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