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?
Correct answer: D. V(x) = 9x(x − 7)
- A. V(x) = x(x + 9)(x + 7)
- B. V(x) = x(x + 9)(x − 7)
- C. V(x) = 9x(x + 7)
- D. V(x) = 9x(x − 7)
Explanation
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).
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