Question**: A right circular cone has a radius of 5 cm and a height of 12 cm. Find the volume of the cone. Use Ï = 3.14.
["# How to Calculate the Volume of a Right Circular Cone: A Step-by-Step Guide", "Understanding the volume of a right circular cone is essential in geometry, particularly when solving problems involving volume formulas. Whether you're a student studying math or someone applying these concepts in real-world scenarios, learning how to calculate the volume of a cone efficiently is a valuable skill.", "## What Is a Right Circular Cone?", "A right circular cone is a three-dimensional shape with a circular base and a single vertex (apex) directly above the center of the base. It is defined by two key measurements: the radius (r) of the base and the height (h), which is the perpendicular distance from the base to the apex.", "---", "## The Volume Formula for a Cone", "The volume ( V ) of a right circular cone can be calculated using the formula:", "[\nV = \frac{1}{3} \pi r^2 h\n]", "Where:\n- ( V ) is the volume,\n- ( r ) is the radius of the base,\n- ( h ) is the height,\n- ( \pi ) (pi) is approximately ( 3.14 ).", "---", "## Applying the Formula to Calculate Volume", "Let’s apply the formula using the given values:\nRadius ( r = 5 , \ ext{cm} )\nHeight ( h = 12 , \ ext{cm} )", "### Step 1: Square the radius\n[\nr^2 = 5^2 = 25 , \ ext{cm}^2\n]", "### Step 2: Multiply by height\n[\nr^2 \cdot h = 25 \ imes 12 = 300 , \ ext{cm}^3\n]", "### Step 3: Multiply by ( \frac{1}{3} \pi )\n[\nV = \frac{1}{3} \ imes 3.14 \ imes 300 = \frac{1}{3} \ imes 942 = 314 , \ ext{cm}^3\n]", "---", "## Final Answer", "The volume of the right circular cone with a radius of 5 cm and a height of 12 cm is:", "[\n\boxed{314 , \ ext{cm}^3}\n]", "---", "## Why This Formula Matters", "Calculating the volume of 3D shapes like cones is useful in engineering, architecture, and everyday life—from estimating materials for construction projects to understanding the capacity of storage containers. Mastering this formula helps you solve practical problems with confidence.", "For quick calculations, always remember:\n[\n\ ext{Volume} = \frac{1}{3} \pi r^2 h\n]\nWith ( \pi \approx 3.14 ), ensuring accuracy becomes easier and faster.", "---", "Start practicing with real-world examples—you’ll be a geometry pro in no time!"]
