A rectangular prism has dimensions of 5 cm by 8 cm by 12 cm. Calculate the surface area of the prism in square centimeters, then determine how many square centimeters of paint are needed to cover the entire surface if 1 liter of paint covers 10,000 square centimeters.
["Calculating the Surface Area of a Rectangular Prism – How Much Paint Do You Need?", "When planning paint jobs for furniture, boxes, or decorative objects, understanding surface area is crucial—and for a rectangular prism, calculating surface area is straightforward. Take, for example, a box with dimensions 5 cm × 8 cm × 12 cm. This popular rectangular prism serves countless real-world applications, from craft projects to storage containers.", "### What Is a Rectangular Prism?", "A rectangular prism is a 3D shape with six rectangular faces, where all angles are right angles, and opposite faces are identical. Its surface area is the total area of all these faces combined.", "### Step 1: Formula for Surface Area", "The surface area ( A ) of a rectangular prism is calculated using:", "[\nA = 2(lw + lh + wh)\n]", "where:\n- ( l ) = length (12 cm)\n- ( w ) = width (8 cm)\n- ( h ) = height (5 cm)", "### Step 2: Plug in the Dimensions", "[\nA = 2 \ imes (5 \ imes 8 + 5 \ imes 12 + 8 \ imes 5)\n]", "Calculate each product:\n- ( 5 \ imes 8 = 40 )\n- ( 5 \ imes 12 = 60 )\n- ( 8 \ imes 5 = 40 )", "Add them:", "[\n40 + 60 + 40 = 140\n]", "Multiply by 2:", "[\nA = 2 \ imes 140 = 280 \ ext{ cm}^2\n]", "### Surface Area Summary:\n- Rectangular prism surface area: 280 square centimeters\nThis means the entire outer surface of the box totals 280 cm².", "### Step 3: Calculate Required Paint", "We now determine how much paint is needed. One liter of paint covers 10,000 cm².", "To find the amount of paint required:", "[\n\ ext{Paint needed (liters)} = \frac{\ ext{Surface area}}{\ ext{Coverage per liter}} = \frac{280}{10,000} = 0.028 \ ext{ liters}\n]", "Convert to milliliters for practical use (1 liter = 1,000 mL):", "[\n0.028 \ imes 1000 = 28 \ ext{ mL}\n]", "### Final Insight:", "To fully coat the rectangular prism with dimensions 5 cm × 8 cm × 12 cm, you need exactly 280 square centimeters of paint surface area, which translates into 28 milliliters of paint. This simple yet precise calculation prevents under-purchasing and ensures a smooth, professional finish.", "Whether you’re painting a bookshelf, a decorative box, or a storage unit, knowing the surface area helps turn craft projects into flawless realities—accurate, efficient, and easy."]
