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Advanced Math / Nonlinear functions Difficulty: Hard

A park ranger hung squirrel houses each in the shape of a right rectangular prism for fox squirrels. Each house has a height of $11$ inches. The length of each house's base is $x$ inches, which is $1$ inch more than the width of the house's base. Which function $V$ gives the volume of each house, in cubic inches, in terms of the length of the house's base?

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Explanation

Choice A is correct. The volume of a prism is equal to the area of its base times its height. It's given that the length of each house's base is $x$ inches and that this length is $1$ inch more than the width, in inches, of the house's base. It follows that the width, in inches, of the house's base is $x minus 1$ . The area of a rectangle is the product of its length and its width. Therefore, the area of the base of the house is $x left parenthesis x minus 1 right parenthesis$ square inches. It's given that the height of each house is $11$ inches. Therefore, the function $V$ that gives the volume of each house, in cubic inches, in terms of the length of the house's base $x$ is $V (x) = x (x - 1) 11$ , or $V (x) = 11 x (x - 1)$ .

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.