A metal rectangular box has external dimensions 20 cm × 12 cm × 5 cm and uniform thickness 1 cm (closed box). Find the volume of metal used.

Introduction / Context:Hollow box problems ask for the volume of material by subtracting inner (hollow) volume from the outer solid volume. With uniform thickness t around all faces, inner dimensions reduce by 2t along each direction for a closed box. This problem builds skill in modeling shells and subtracting volumes.

Given Data / Assumptions:

• External: 20 × 12 × 5 cm.
• Thickness t = 1 cm; closed rectangular box (has a lid).
• Inner dimensions: (20 − 2) × (12 − 2) × (5 − 2) = 18 × 10 × 3 cm.

Concept / Approach:Volume of metal = V_outer − V_inner. Compute each cuboid volume and subtract. The numbers are exact integers.

Step-by-Step Solution:V_outer = 20 * 12 * 5 = 1200 cm^3V_inner = 18 * 10 * 3 = 540 cm^3Volume of metal = 1200 − 540 = 660 cm^3

Verification / Alternative check:If the box were open at one end, inner reduction would differ for one face; here “box” with no contrary note implies closed, matching the subtraction used.

Why Other Options Are Wrong:550, 656, and 475 cm^3 do not equal the precise difference; they might come from reducing only some dimensions or arithmetic slips.

Common Pitfalls:Forgetting to reduce by 2t in each dimension; treating it as an open box unintentionally; unit confusion.

Final Answer:660 cm3