The volume of a cylinder is 500 cubic units, and its height is 10 units. Find the radius of the base.
["How to Calculate the Radius of a Cylinder Given Its Volume and Height", "Understanding the geometry of a cylinder is essential in many fields, from engineering to architecture. One common problem involves determining the radius of the base when the volume and height are known. In this article, we’ll explore how to find the radius of a cylinder whose volume is 500 cubic units and whose height is 10 units.", "### Understanding the Formula for a Cylinder’s Volume", "The volume ( V ) of a cylinder is calculated using the formula:", "[\nV = \pi r^2 h\n]", "Where:\n- ( V ) = volume\n- ( r ) = radius of the circular base\n- ( h ) = height of the cylinder", "Given:\n- Volume ( V = 500 ) cubic units\n- Height ( h = 10 ) units", "### Step-by-Step Calculation", "Start with the volume formula:", "[\n500 = \pi r^2 \cdot 10\n]", "Divide both sides by 10 to simplify:", "[\n50 = \pi r^2\n]", "Now, solve for ( r^2 ):", "[\nr^2 = \frac{50}{\pi}\n]", "Take the square root of both sides to find ( r ):", "[\nr = \sqrt{\frac{50}{\pi}}\n]", "### Numerical Calculation (Optional)", "Using ( \pi \approx 3.1416 ):", "[\nr = \sqrt{\frac{50}{3.1416}} \approx \sqrt{15.92} \approx 3.99\n]", "So, the radius is approximately 4 units.", "### Conclusion", "Knowing how to calculate the radius from the cylinder’s volume and height is a practical skill. For a cylinder with a volume of 500 cubic units and a height of 10 units, the radius of the base is:", "[\nr = \sqrt{\frac{50}{\pi}} \approx 4 \ ext{ units}\n]", "This method ensures precision in design, construction, and analysis involving cylindrical shapes. Whether you're designing a water tank, a pipe, or a scientific model, mastering this formula is invaluable.", "---", "Keywords: radius of cylinder, volume of cylinder formula, calculate radius from volume and height, cylinder geometry, volume calculation formula, find cylinder radius, ( V = \pi r^2 h ), radius of a cylinder 500 cubic units, cylinder height 10 units radius", "Meta Description: Learn how to find the radius of a cylinder with a volume of 500 cubic units and height of 10 units using the volume formula ( V = \pi r^2 h ). Perfect for students, engineers, and DIY calculators."]
