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A 10-gallon aquarium is 3 inches higher than it is wide. Its length is 16 inches, and its volume is 4320 cubic inches. What are the height and width of the aquarium?

Answer :

Final answer:

The width of the aquarium is found to be 15 inches by solving the quadratic equation W^2 + 3W - 270 = 0. The height, being 3 inches more than the width, is consequently 18 inches.

Explanation:

To find the height and width of a 10-gallon aquarium with the given volume of 4320 inches cubed, its length of 16 inches, and the information that its height is 3 inches more than its width, we can use the formula for the volume of a rectangular prism: volume = length × width × height. The question tells us that the volume (V) is 4320 in.3 and the length (L) is 16 in.

Let's denote the width of the aquarium as W, and the height of the aquarium as H. We know from the problem that H = W + 3 inches. Using the volume formula V = L × W × H and substituting the provided values we get: 4320 in.3 = 16 in. × W × (W + 3 in.). To solve this equation, we first simplify it:

  • 4320 = 16W(W + 3)
  • 4320 = 16W2 + 48W
  • 270 = W2 + 3W
  • W2 + 3W - 270 = 0

Solving this quadratic equation, we find the factorable form is (W + 18)(W - 15) = 0, leading to two possible solutions for W, which are W = -18 or W = 15. However, since we cannot have a negative width, W = 15 inches.

The height, which is 3 inches taller than the width, will therefore be H = W + 3 = 15 in. + 3 in. = 18 in.

The aquarium's width is 15 inches, and its height is 18 inches.

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