A right rectangular prism has a height of 9 inches. The length of the prism's base is x inches, which

Question

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?

A.

$V (x) = 9 x (x - 7)$

B.

$V (x) = x (x + 9) (x + 7)$

C.

$V (x) = x (x + 9) (x - 7)$

D.

$V (x) = 9 x (x + 7)$

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 = 9 x 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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