A cone has a radius of 3 cm and a slant height of 5 cm. Calculate the lateral surface area.
["Title: How to Calculate the Lateral Surface Area of a Cone: A Step-by-Step Guide", "When studying geometry, understanding the properties of three-dimensional shapes is essential—and the cone is one fascinating figure with practical applications in real life, from traffic cones to decorative storefronts. If you’ve been asked to calculate the lateral surface area of a cone with a given radius and slant height, this article will walk you through the process using a clear example.", "In this case, we focus on a cone with a radius of 3 cm and a slant height of 5 cm. Whether you're preparing for a math exam or simply want to master surface area calculations, breaking down the formula makes the task manageable.", "---", "### Understanding the Cone and Its Dimensions", "A cone is a three-dimensional shape with a circular base and a single curved surface that meets at a point called the apex. To calculate the lateral surface area (the curved part of the cone, excluding the base), we use the formula:", "[\n\ ext{Lateral Surface Area} = \pi r l\n]", "Where:\n- ( r ) = radius of the base\n- ( l ) = slant height\n- ( \pi ) ≈ 3.1416 (pi)", "---", "### Applying the Formula with Given Dimensions", "Given:\n- Radius ( r = 3 ) cm\n- Slant height ( l = 5 ) cm", "Plugging these values into the formula:", "[\n\ ext{Lateral Surface Area} = \pi \ imes 3 \ imes 5 = 15\pi , \ ext{cm}^2\n]", "To express this numerically:\n[\n15\pi \approx 15 \ imes 3.1416 = 47.124 , \ ext{cm}^2\n]", "---", "### Interpretation and Practical Use", "The lateral surface area of the cone measures approximately 47.12 cm². This value represents the total area of the cone’s curved surface; it’s essential for calculating materials needed for construction or manufacturing cone-shaped objects.", "---", "### Summary", "To summarize:\n- Use ( \pi r l ) to compute the lateral surface area of a cone.\n- Substitute ( r = 3 , \ ext{cm} ) and ( l = 5 , \ ext{cm} ).\n- Final result: ( 15\pi , \ ext{cm}^2 ) (≈ 47.12 cm²).", "Understanding this calculation not only strengthens your geometry knowledge but also applies directly to fields such as engineering, art, and design. Start practicing with different radius and slant height combinations, and mastering the lateral surface area of cones will become second nature.", "---", "Key Takeaways:\n- Lateral surface area of a cone: ( \pi r l )\n- Radius = 3 cm, slant height = 5 cm → ( 15\pi , \ ext{cm}^2 )\n- Makes practical real-world problem-solving easier", "---", "Explore more geometry tips and calculations to build confidence in mathematical reasoning and apply it confidently in school and beyond!"]
