A cone has a base radius of 4 cm and a height of 9 cm. Calculate its volume.
["# How to Calculate the Volume of a Cone: A Practical Example", "Understanding geometric shapes is essential in mathematics, engineering, architecture, and design — and few shapes are as iconic as the cone. From ice cream cones to traffic signs, cones are everywhere. But one of the most fundamental questions when studying cones is: how do you compute their volume? In this article, we’ll explore the formula for the volume of a cone and apply it to a specific case: a cone with a base radius of 4 cm and a height of 9 cm.", "## The Cone Volume Formula", "The volume ( V ) of a right circular cone is calculated using the formula:", "[\nV = \frac{1}{3} \pi r^2 h\n]", "Where:\n- ( r ) = radius of the base\n- ( h ) = height (or vertical depth) of the cone\n- ( \pi \approx 3.1416 ) (pi)", "This formula arises from the fact that a cone is one-third the volume of a corresponding cylinder with the same base and height.", "## Applying the Formula to the Given Dimensions", "We are given:\n- Base radius ( r = 4 ) cm\n- Height ( h = 9 ) cm", "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 ( \frac{1}{3} \pi ).\n[\nV = \frac{1}{3} \ imes \pi \ imes 144 = \frac{144}{3} \pi = 48\pi \ ext{ cm}^3\n]", "Using ( \pi \approx 3.1416 ):", "[\nV \approx 48 \ imes 3.1416 = 150.7968 \ ext{ cm}^3\n]", "## Final Result", "The volume of a cone with a base radius of 4 cm and a height of 9 cm is approximately:", "150.8 cm³ (to one decimal place)", "---", "## Why This Matters", "Calculating the volume of cones is not just an academic exercise. Engineers use it to design containers and structural supports. Architects apply it in dome and pyramid structures. Students learning geometry benefit from concrete examples like this one. Understanding how to compute the volume helps build a deeper grasp of three-dimensional math and real-world applications.", "If you’re studying geometry, designing models, or working in a field that involves spatial calculations, knowing the cone volume formula and how to apply it is a valuable skill.", "---", "Key takeaway:\nThe volume of a cone with radius 4 cm and height 9 cm is ( 48\pi , \ ext{cm}^3 ), or about 150.8 cm³. Use the formula ( V = \frac{1}{3} \pi r^2 h ) to compute volumes confidently and accurately."]
