A rectangular prism has dimensions 4 cm, 5 cm, and 6 cm. If the dimensions are scaled by a factor of 2, what is the new volume?
["Title: Scaling a Rectangular Prism: How Volume Changes When Dimensions Double", "When working with geometric shapes, understanding how scaling affects volume is essential. In this article, we explore what happens to the volume of a rectangular prism when its dimensions are scaled by a factor of 2, using a specific example: a prism measuring 4 cm, 5 cm, and 6 cm.", "Original Dimensions and Volume Calculation", "The original dimensions of the rectangular prism are:\n- Length = 4 cm\n- Width = 5 cm\n- Height = 6 cm", "Volume of a rectangular prism is calculated using the formula:\n[\n\ ext{Volume} = \ ext{length} \ imes \ ext{width} \ imes \ ext{height}\n]", "Substituting the values:\n[\n\ ext{Original Volume} = 4 \ imes 5 \ imes 6 = 120 \ ext{ cm}^3\n]", "Scaling the Dimensions by a Factor of 2", "Now, if all dimensions are scaled by a factor of 2, the new dimensions become:\n- Length = 4 × 2 = 8 cm\n- Width = 5 × 2 = 10 cm\n- Height = 6 × 2 = 12 cm", "Calculate the new volume:\n[\n\ ext{New Volume} = 8 \ imes 10 \ imes 12 = 960 \ ext{ cm}^3\n]", " Amazing Relationship Between Scaling and Volume", "Notice that doubling each dimension did not simply double the volume—it quadrupled it to 960 cm³. This reflects a fundamental principle in geometry: volume scales with the cube of the linear scaling factor.", "Mathematically, when all dimensions are multiplied by a factor ( k ), the new volume becomes:\n[\n\ ext{New Volume} = k^3 \ imes \ ext{Original Volume}\n]", "Here, ( k = 2 ), so:\n[\n\ ext{New Volume} = 2^3 \ imes 120 = 8 \ imes 120 = 960 \ ext{ cm}^3\n]", "Why This Matters", "Understanding volume scaling is crucial in real-world applications, from engineering and architecture to packaging and manufacturing. When designing or modifying objects, knowing how dimensions affect volume helps optimize space, materials, and costs efficiently.", "Conclusion", "A rectangular prism with dimensions 4 cm × 5 cm × 6 cm has an original volume of 120 cm³. After scaling each dimension by a factor of 2, the new volume becomes 960 cm³—a striking example of how volume increases threefold in linear terms. This insight empowers better mathematical reasoning and practical problem-solving in various STEM fields.", "Keywords: rectangular prism volume, scaling dimensions, geometric scaling, volume calculation, cubed scaling factor, mathematical relationships, volume scaling principle, 4 cm × 5 cm × 6 cm, doubling dimensions, 960 cm³, geometry problems, cube scaling."]
