A rectangular prism has a volume of 240 cubic inches, a length of 10 inches, and a width of 6 inches. Find the height.
["Finding the Height of a Rectangular Prism with a Volume of 240 Cubic Inches", "Understanding the dimensions of geometric shapes is essential in fields like architecture, engineering, and everyday problem-solving. One of the most frequently encountered shapes is the rectangular prism, and calculating its height when given the volume, length, and width is a common task.", "In this article, we’ll explore how to find the height of a rectangular prism using real-world dimensions. Specifically, we’ll solve the problem: A rectangular prism has a volume of 240 cubic inches, a length of 10 inches, and a width of 6 inches. What is the height?", "---", "### What Is a Rectangular Prism?", "A rectangular prism is a three-dimensional shape with six rectangular faces. Its volume is calculated using the formula:", "[\n\ ext{Volume} = \ ext{Length} \ imes \ ext{Width} \ imes \ ext{Height}\n]", "This formula is fundamental when dealing with prisms, ensuring accurate volume calculations for storage, shipping, construction, and educational purposes.", "---", "### Given Measurements", "From the problem:", "- Volume = 240 cubic inches\n- Length = 10 inches\n- Width = 6 inches\n- Height = ? (to be found)", "---", "### Step-by-Step Calculation", "Start with the volume formula:", "[\n\ ext{Volume} = \ ext{Length} \ imes \ ext{Width} \ imes \ ext{Height}\n]", "Substitute the known values:", "[\n240 = 10 \ imes 6 \ imes \ ext{Height}\n]", "Multiply the length and width:", "[\n240 = 60 \ imes \ ext{Height}\n]", "Now solve for the height by dividing both sides by 60:", "[\n\ ext{Height} = \frac{240}{60} = 4\n]", "---", "### The Result", "The height of the rectangular prism is 4 inches.", "---", "### Why This Matters", "Knowing how to deduce missing dimensions using the volume formula is valuable in many contexts:\n- Packing and shipping require accurate volume and height to maximize container usage.\n- Construction professionals rely on this principle to ensure structural integrity and space efficiency.\n- Students mastering geometry gain confidence through hands-on application of formulas.", "---", "### Final Summary", "When a rectangular prism has a volume of 240 cubic inches, a length of 10 inches, and a width of 6 inches, the height is determined by rearranging the volume formula:", "[\n\ ext{Height} = \frac{\ ext{Volume}}{\ ext{Length} \ imes \ ext{Width}} = \frac{240}{10 \ imes 6} = 4 \ ext{ inches}\n]", "This simple yet powerful method helps solve real-world spatial problems effectively.", "---", "Keywords for SEO: rectangular prism volume, find height, volume formula, geometric calculations, 10 inch length, 6 inch width, rectangular prism dimensions, how to calculate height, geometry problem solved, cubic inch volume, prism math."]
