Una lata cilíndrica tiene una altura de 10 cm y un diámetro de 6 cm. ¿Cuál es su volumen?
["Formula Calculating the Volume of a Cylindrical Can: How to Compute It with a 10 cm Height and 6 cm Diameter", "When dealing with cylindrical containers—such as a simple metal or tin can—one of the most useful mathematical concepts is calculating its volume. Whether you're designing packaging, planning storage, or simply curious about everyday geometry, knowing how to find the volume of a cylinder is essential. In this article, we explore how to compute the volume of a cylindrical can with a height of 10 cm and a diameter of 6 cm, step by step.", "### What Is a Cylinder?", "A cylinder is a three-dimensional shape with two identical circular bases connected by a curved surface. The volume of a cylinder represents the amount of space it occupies and is determined by the product of the area of its circular base and its height.", "### Formula for the Volume of a Cylinder", "[\n\ ext{Volume} = \pi r^2 h\n]", "Where:\n- ( r ) is the radius of the base\n- ( h ) is the height of the cylinder\n- ( \pi \approx 3.1416 ) is the mathematical constant pi", "---", "### Step 1: Identify Given Measurements", "From the problem:\n- Height (( h )) = 10 cm\n- Diameter = 6 cm", "To use the volume formula, we need the radius (( r )), which is half the diameter:", "[\nr = \frac{\ ext{diameter}}{2} = \frac{6\ \ ext{cm}}{2} = 3\ \ ext{cm}\n]", "---", "### Step 2: Apply the Formula", "Now substitute ( r = 3 ) cm and ( h = 10 ) cm into the volume formula:", "[\n\ ext{Volume} = \pi \ imes (3)^2 \ imes 10 = \pi \ imes 9 \ imes 10 = 90\pi\ \ ext{cm}^3\n]", "---", "### Step 3: Calculate Numerical Value", "Using ( \pi \approx 3.1416 ):", "[\n90\pi \approx 90 \ imes 3.1416 = 282.744\ \ ext{cm}^3\n]", "---", "### Conclusion: Volume of the Can", "A cylindrical can with a height of 10 cm and a diameter of 6 cm has a volume of approximately 282.74 cm³.", "---", "### Why This Matters", "Understanding how to calculate a cylinder’s volume helps in real-world applications such as food packaging, manufacturing, and logistics. This simple formula allows quick estimation and accurate design, ensuring efficient use of space and materials.", "Keywords: volume of a cylinder, calculate cylinder volume, formula for volume cylinder, volume of cylindrical can, cylinder geometry, 10 cm cylinder height, 6 cm diameter can", "---", "Summary:\nFor a cylindrical can of height 10 cm and diameter 6 cm (radius 3 cm), the volume is ( 90\pi ) cm³ or about 282.74 cm³. This calculation is quick, essential, and widely applicable in practical and educational contexts."]
