A rectangular box has dimensions 2 in by 4 in by 4 in. Increasing each dimension of the box by the same amount yields a new box with volume seven times the old. Use the ALEKS graphing calculator to find how much each dimension of the original box was increased to create the new box. Round your answer to two decimal places.
Answer
Final Answer: The amount each dimension of the original box was increased to create the new box is approximately \(\boxed{2.82}\) inches.
Step 1 ：The volume of a rectangular box is given by the formula \(V = lwh\), where \(l\), \(w\), and \(h\) are the length, width, and height of the box, respectively. In this case, the original box has dimensions 2 in by 4 in by 4 in, so its volume is \(V = 2*4*4 = 32\) cubic inches.
Step 2 ：The problem states that each dimension of the box is increased by the same amount, \(x\), to create a new box with volume seven times the old. This means the new box has dimensions \((2+x)\) in by \((4+x)\) in by \((4+x)\) in, and its volume is \(V' = (2+x)(4+x)(4+x) = 7*V = 7*32 = 224\) cubic inches.
Step 3 ：We can set up the equation \((2+x)(4+x)(4+x) = 224\) and solve for \(x\).
Step 4 ：The solution to the equation is a list of three complex numbers. However, in the context of this problem, the dimension of a box cannot be a complex number. Therefore, we need to find the real root of the equation.
Step 5 ：Final Answer: The amount each dimension of the original box was increased to create the new box is approximately \(\boxed{2.82}\) inches.
