This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Determine the dimensions of the original metal sheet. Let the width of the rectangular metal sheet be W and its length be L. The problem states that the length is twice its width: L = 2W. It also states that the width of the metal sheet was 8 cm. So, W = 8 cm. Then, the length of the metal sheet is L = 2 × 8 = 16 cm. Step 2: Determine the dimensions of the tank's base and height. Squares of side length x cm are cut from each of the four corners. When the sides are folded up, these cut squares determine the height of the tank. Height of the tank, h = x cm. The length of the base of the tank will be the original length minus 2x (since x is removed from both ends): Length of the base, l_tank = L - 2x = 16 - 2x cm. The width of the base of the tank will be the original width minus 2x: Width of the base, w_tank = W - 2x = 8 - 2x cm. Note: For a valid tank to be formed, x must be greater than 0, and both 16-2x and 8-2x must be positive. This implies x < 4. The statement "cutting equal squares of length 6 cm" in the problem description is inconsistent with the width of 8 cm, as x=6 would lead to a negative width (8-2(6) = -4). Therefore, we treat x as a variable for the cut square side length as requested