Question

Your principal surprises you by buying your class a turtle. He brings the turtle to your class along with a sheet from the pet store titled "Turtle Tank Rule."

*Tank walls must be at least 1 foot tall so the turtle can't climb out.

*There must be at least 400 square inches of floor space for the turtle to walk around on.

Your teacher says the volume of the tank must be smaller than 5000 cubic inches so it doesn't take up too much room in the classroom.

Give the dimensions of a tank that would work for your new turtle. Use words and numbers to explain how your tank satisfies the "Turtle Tank Rules" and your teacher requirements.

Volume of a rectangular prism= length X width X height

Answer 1

The height of the tank must be at least 1 foot, or 12 inches. We know the floor area (which is length x width) must be at least 400 inches. Therefore these minimum dimensions already tell us that the minimum volume is 400 x 12 = 4800 cubic inches. Since we have a maximum of 5000 cubic inches, the volume must be within the range of 4800 - 5000 cubic inches.

We can set the height at exactly 1 ft (or 12 inches). Then we can select length and width that multiply to 400 square inches, for example, L = 40 inches and W = 10 in. This gives us a tank of dimensions 40 x 10 x 12 = 4800 cubic inches, which fits all the criteria.