A cone has a base radius of 4 cm and height 9 cm. What is its volume? (Use \( V = \frac{1}{3}\pi r^2 h \))

["Title: Calculate the Volume of a Cone: A Step-by-Step Guide with Radius 4 cm & Height 9 cm", "Meta Description: Learn how to calculate the volume of a cone with a base radius of 4 cm and height of 9 cm using the formula ( V = \frac{1}{3}\pi r^2 h ). Simple math for precise results.", "---", "When studying geometry, understanding the volume of a cone is a fundamental skill. Whether you're solving textbook problems or tackling real-world shapes like traffic cones, washing machines, or ice cream cones, knowing how to calculate volume efficiently is essential. In this guide, we’ll focus on a specific cone with a base radius of 4 cm and a height of 9 cm, and walk through the steps using the formula:", "[\nV = \frac{1}{3}\pi r^2 h\n]", "### What is Cone Volume?\nThe volume of a cone measures the amount of space it occupies. Unlike a cylinder with a simple rectangular prism formula, a cone uses one-third of the base area multiplied by its height—this geometric relationship arises from its tapering shape.", "---", "### Plugging in the Values\nGiven:\n- Radius ( r = 4 ) cm\n- Height ( h = 9 ) cm", "Start with the formula:\n[\nV = \frac{1}{3} \pi r^2 h\n]", "1. Square the radius:\n[\nr^2 = 4^2 = 16 , \ ext{cm}^2\n]", "2. Multiply by height and (\pi):\n[\nV = \frac{1}{3} \pi (16) (9)\n]", "3. Multiply constants step-by-step:\nFirst compute ( 16 \ imes 9 = 144 ), so:\n[\nV = \frac{1}{3} \pi \ imes 144\n]", "4. Divide by 3:\n[\nV = 48\pi , \ ext{cm}^3\n]", "---", "### Final Answer with Approximation\nSince ( \pi \approx 3.1416 ), the approximate volume is:\n[\nV \approx 48 \ imes 3.1416 = 150.8 , \ ext{cm}^3\n]", "But unrounded, the exact volume is:\n[\n\boxed{48\pi , \ ext{cm}^3}\n]", "---", "### Why Accuracy Matters\nWhile rounding gives a quick approximation, using ( \pi ) keeps calculations precise—especially in engineering, construction, or manufacturing. For this cone, knowing the exact volume helps ensure compatibility with storage units or weight-based calculations.", "Try applying this formula to other cones: changing the radius or height instantly adjusts the calculation, showing the elegance and utility of this geometric principle. Whether for classroom success or practical use, mastering cone volume starts here.", "---", "Keywords: cone volume, formula ( V = \frac{1}{3}\pi r^2 h ), calculate cone volume, radius 4 cm, height 9 cm, geometry tutorial, formula steps", "---", "By understanding how radius and height influence volume, you gain insight into one of the most widely applicable formulas in math and science—perfect for students, teachers, and DIY enthusiasts alike!"]