Given \( r = 3 \) meters and \( h = 5 \) meters, substitute and calculate:
["Understanding the Cone Formula: Calculating Volume Given ( r = 3 ) m and ( h = 5 ) m", "When working with conical shapes in geometry, one of the most essential calculations is determining the volume. Whether for engineering, architecture, or educational purposes, knowing how to use the cone volume formula is crucial. This article guides you step-by-step through substituting real-world values—specifically when the radius ( r = 3 ) meters and height ( h = 5 ) meters—into the formula and interpreting the result.", "### What Is the Volume of a Cone?", "The volume ( V ) of a right circular cone is given by the formula:", "[\nV = \frac{1}{3} \pi r^2 h\n]", "Where:\n- ( r ) is the radius of the base,\n- ( h ) is the height,\n- ( \pi \approx 3.1416 )", "This formula reflects that a cone holds one-third the volume of a cylinder with the same base and height, inspired by Archimedes’ discovery.", "### Step 1: Substitute Given Values", "Given ( r = 3 ) m and ( h = 5 ) m, substitute these into the formula:", "[\nV = \frac{1}{3} \pi (3)^2 (5)\n]", "First, square the radius:", "[\n(3)^2 = 9\n]", "Now multiply:", "[\nV = \frac{1}{3} \pi \ imes 9 \ imes 5\n]", "[\nV = \frac{1}{3} \pi \ imes 45\n]", "[\nV = 15\pi \ ext{ m}^3\n]", "### Step 2: Calculate the Numerical Value", "Using ( \pi \approx 3.1416 ):", "[\nV \approx 15 \ imes 3.1416 = 47.124 \ ext{ m}^3\n]", "Thus, the volume is approximately 47.12 cubic meters.", "### Why Does This Matter?", "Knowing how to compute the volume of a cone is vital in fields like construction, where conical tanks or silos must be sized for capacity. By plugging in measurable dimensions such as ( r = 3 ) m and ( h = 5 ) m, engineers and designers can accurately estimate storage volumes, ensuring efficiency and safety in design.", "### Summary", "- Formula: ( V = \frac{1}{3} \pi r^2 h )\n- Substitute ( r = 3 ), ( h = 5 ):\n[\nV = \frac{1}{3} \pi (3)^2 (5) = 15\pi \ ext{ m}^3\n]\n- Approximate volume: ( V \approx 47.12 \ ext{ m}^3 )", "With these simple substitutions and calculations, anyone can determine the volume of a cone—a fundamental tool in both math and applied sciences.", "---", "Keywords: cone volume formula, calculate cone volume, geometry formula, calculate cone with r=3m, calculate cone with h=5m, volume of a cone, cone volume calculator, math formula substitution, 3 meter radius cone, 5 meter height cone, cone formula application", "Meta Title: How to Calculate Cone Volume: Step-by-Step with r = 3 m and h = 5 m\nMeta Description: Learn to calculate the volume of a cone with radius 3 meters and height 5 meters using the formula ( V = \frac{1}{3} \pi r^2 h ), with step-by-step substitution and calculation."]
