A rectangular prism has dimensions 8 cm by 6 cm by 10 cm. If a cube with side length 4 cm is removed from one corner, what is the remaining volume of the prism?

["Rectangular Prism With Removed Cube: Calculating Remaining Volume", "When working with geometric shapes, understanding how modifications like removing parts from a solid affect its total volume is essential. In this article, we explore the case of a rectangular prism from which a cube is removed from a corner, focusing on calculating the remaining volume accurately.", "We begin with a rectangular prism measuring 8 cm by 6 cm by 10 cm. First, we compute the original volume using the standard formula for a rectangular prism:", "[\n\ ext{Volume}{\ ext{prism}} = \ ext{length} \ imes \ ext{width} \ imes \ ext{height}\n]", "Substituting the given dimensions:", "[\n\ ext{Volume}^3}} = 8 \ imes 6 \ imes 10 = 480 \ ext{ cm\n]", "Next, a cube with a side length of 4 cm is removed from one corner of the prism. To determine the volume removed, we use the cube volume formula:", "[\n\ ext{Volume}{\ ext{cube}} = \ ext{side}^3 = 4^3 = 64 \ ext{ cm}^3\n]", "Now, subtract the removed cube’s volume from the original prism volume to find the remaining volume:", "[\n\ ext{Remaining Volume} = \ ext{Volume}^3}} - \ ext{Volume}_{\ ext{cube}} = 480 - 64 = 416 \ ext{ cm\n]", "Conclusion: After removing a 4 cm cubic section from the corner of the original rectangular prism (dimensions 8 cm × 6 cm × 10 cm), the remaining volume is 416 cm³. This calculation helps in material estimation, packaging design, and structural modeling—making it a practical application for students, architects, and engineers alike.", "---", "This approach ensures clarity in geometric change calculations and supports real-world problem-solving involving volume reduction through corner removal."]