Jenny uses small boxes to ship the earrings she sells on her jewelry website. The box is in the shape of a rectangular prism and has a volume of 8 cubic inches. The length of the box is 2 inches. The height of the box is 3 inches more than the width. Complete the equation that models the volume of the box in terms of the width, x. Volume of a prism (V) = (length)(width)(height)
SAT · Middle School · Thu Feb 04 2021
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Answer: To find the equation that models the volume of the box in terms of the width (x), let's use the volume formula for a rectangular prism which is V = length × width × height. We know the volume (V) is 8 cubic inches, the length is 2 inches, and the height (h) is 3 inches more than the width. Therefore, h = x + 3.
Now, let's set up the equation with the known values:
V = length × width × height 8 = 2 × x × (x + 3)
Simplifying the equation further:
8 = 2x(x + 3)
So, the equation that models the volume of the box in terms of the width, x, is:
8 = 2x^2 + 6x