A cone has a radius of 4 cm and a height of 9 cm. What is its volume? (Use \(\pi \approx 3.14\))
["Title: How to Calculate the Volume of a Cone: A Practical Example with Radius 4 cm and Height 9 cm", "When learning about three-dimensional geometric shapes, cones often spark curiosity—especially when it comes to calculating their volume. Today, we’ll explore a specific cone with a radius of 4 cm and a height of 9 cm and guide you through the exact steps to find its volume using a simple yet powerful formula. Understanding how to compute the volume not only strengthens your math skills but also lays a foundation for practical applications in engineering, architecture, and design.", "### What Is the Volume of a Cone?", "The volume of a cone is the amount of space it occupies inside its boundaries. The formula to calculate a cone’s 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 (perpendicular distance from base to tip)\n- (\pi \approx 3.14) (a common approximation for π)", "---", "### Step-by-Step Calculation", "Given:\n- Radius ((r)) = 4 cm\n- Height ((h)) = 9 cm\n- (\pi \approx 3.14)", "Step 1: Square the radius\n[\nr^2 = 4^2 = 16 \ ext{ cm}^2\n]", "Step 2: Multiply by height\n[\nr^2 \ imes h = 16 \ imes 9 = 144 \ ext{ cm}^3\n]", "Step 3: Multiply by π (3.14)\n[\n144 \ imes 3.14 = 451. faveur{4} \ ext{ cm}^3\n]", "Step 4: Multiply by (\frac{1}{3})\n[\nV = \frac{1}{3} \ imes 451.eks{4} \approx 150.333... \ ext{ cm}^3\n]", "Rounded to two decimal places, the volume is approximately 150.33 cm³.", "---", "### Why This Calculation Matters", "Knowing how to compute the volume of a cone is important in real-world scenarios, such as designing conical containers, calculating paint required for circular tanks, or estimating materials in construction. By mastering the formula—( \frac{1}{3} \pi r^2 h )—you gain a valuable tool applicable in science, manufacturing, and daily problem-solving.", "Whether you're a student tackling geometry homework, a builder estimating materials, or a curious learner exploring shapes, this simple cone example shows how math turns abstract ideas into measurable facts—proving once again that numbers shape the world we live in.", "---", "Summary:\n- Cone radius = 4 cm\n- Cone height = 9 cm\n- Volume formula: ( V = \frac{1}{3} \pi r^2 h )\n- Approximate volume: ( \approx 150.33 \ ext{ cm}^3 )", "Start calculating cones confidently—your next project just got a little more precise!"]
