A cone has a radius of 3 cm and a height of 4 cm. What is its volume? Use the formula \( V = rac{1}{3}\pi r^2 h \).
["# What Is the Volume of a Cone with Radius 3 cm and Height 4 cm?", "Understanding the volume of a cone is essential in geometry, engineering, architecture, and everyday calculations involving 3D shapes. In this article, we’ll explore how to calculate the volume of a cone with specific dimensions—radius of 3 cm and height of 4 cm—using the correct mathematical formula.", "## What Is a Cone’s Volume?", "The volume of a cone represents the amount of space it occupies. The formula to calculate this volume is:", "[\nV = \frac{1}{3} \pi r^2 h\n]", "where:\n- ( V ) = volume\n- ( r ) = radius of the circular base\n- ( h ) = height of the cone\n- ( \pi ) ≈ 3.1416 (pi)", "This formula accounts for the conical shape, which tapers uniformly from a circular base to a point (the apex).", "## Given Dimensions", "For the cone in this example:\n- Radius ( r = 3 ) cm\n- Height ( h = 4 ) cm", "## Step-by-Step Volume Calculation", "1. Plug values into the formula:\n[\nV = \frac{1}{3} \pi (3)^2 (4)\n]", "2. Calculate the square of the radius:\n[\n3^2 = 9\n]", "3. Multiply by the height:\n[\n9 \ imes 4 = 36\n]", "4. Multiply by ( \frac{1}{3} ):\n[\n\frac{1}{3} \ imes 36 = 12\n]", "5. Multiply by ( \pi ):\n[\nV = 12\pi\n]", "## Approximate Value", "Using ( \pi \approx 3.1416 ),\n[\nV \approx 12 \ imes 3.1416 = 37.70 \ ext{ cm}^3\n]", "So, the volume of the cone is approximately 37.70 cubic centimeters.", "## Why Use This Formula?", "The ( \frac{1}{3} \pi r^2 h ) formula reflects how a cone holds one-third the volume of a cylinder with the same base and height. This principle is crucial in design, storage capacity estimation, and scientific applications involving conical shapes.", "## Conclusion", "Knowing how to calculate a cone’s volume is simple with the right formula. For a cone with a radius of 3 cm and a height of 4 cm, the volume is:", "[\nV = 12\pi \ ext{ cm}^3 \approx 37.70 \ ext{ cm}^3\n]", "Understanding and applying this formula helps in solving real-life problems—from calculating material needs to geometry assignments—making it a fundamental skill in math and science."]
