For as long as she can remember, Beth has had a ton of pet fish. She is in the market for a new fish tank shaped like a rectangular prism which she wants to hold 75 gallons, or 17,325 cubic inches, of water. She wants the fish tank to be 48 inches long to fit perfectly along her wall, and she wants the tank to be twice as tall as it is wide.To the nearest tenth of an inch, how wide and tall should the tank be? inches wide and inches tall
Question
For as long as she can remember, Beth has had a ton of pet fish. She is in the market for a new fish tank shaped like a rectangular prism which she wants to hold 75 gallons, or 17,325 cubic inches, of water. She wants the fish tank to be 48 inches long to fit perfectly along her wall, and she wants the tank to be twice as tall as it is wide.To the nearest tenth of an inch, how wide and tall should the tank be? inches wide and inches tall
Solution
The volume of a rectangular prism (or a fish tank in this case) is given by the formula: length x width x height. We know the volume (17,325 cubic inches), the length (48 inches), and that the height is twice the width. We can set up the equation and solve for width and height.
Let's denote the width as w. Then the height will be 2w.
So, we have: 48 * w * 2w = 17,325
Solving this equation gives:
96w^2 = 17,325 w^2 = 17,325 / 96 w^2 = 180.47
Taking the square root of both sides gives:
w = sqrt(180.47) = 13.4 inches (to the nearest tenth of an inch)
Then the height would be 2w = 2 * 13.4 = 26.8 inches (to the nearest tenth of an inch)
So, the fish tank should be approximately 13.4 inches wide and 26.8 inches tall.
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