A cone has a base radius of 4 cm and a slant height of 5 cm. What is its lateral surface area?
["Lateral Surface Area of a Cone: A Step-by-Step Guide (Base Radius = 4 cm, Slant Height = 5 cm)", "When working with geometric shapes like cones, understanding their surface areas is essential—especially for students, engineers, architects, or anyone studying 3D geometry. Whether you're designing a conical structure or solving math problems, knowing the lateral surface area of a cone helps in calculations involving materials, coatings, or surface measurements.", "In this article, we’ll explore how to calculate the lateral surface area of a cone with a base radius of 4 cm and a slant height of 5 cm—a common problem in both academic and practical applications.", "---", "### What Is a Cone and Its Lateral Surface Area?", "A cone is a three-dimensional geometric shape with a circular base and a single curved surface that tapers to a point, called the apex. The lateral surface area refers only to the outer curved part of the cone—the area of the surface excluding the circular base.", "The formula to calculate the lateral surface area (LSA) of a cone is:", "[\n\ ext{Lateral Surface Area} = \pi r l\n]", "where:\n- ( r ) = radius of the base\n- ( l ) = slant height (the distance from the base edge to the apex along the cone’s side)", "---", "### Applying the Formula with Given Values", "Given:\n- Base radius ( r = 4 ) cm\n- Slant height ( l = 5 ) cm", "Plug the values into the formula:", "[\n\ ext{Lateral Surface Area} = \pi \ imes 4 \ imes 5 = 20\pi , \ ext{cm}^2\n]", "---", "### Final Result", "Using ( \pi \approx 3.1416 ), the numerical value is approximately:", "[\n20\pi \approx 62.83 , \ ext{cm}^2\n]", "However, keeping the answer in exact terms is preferred in technical and academic contexts:", "[\n\ ext{Lateral Surface Area} = 20\pi , \ ext{cm}^2\n]", "---", "### Why Does This Matter?", "Knowing the lateral surface area of a cone aids in various real-world applications:", "- Manufacturing: To calculate paint or material needed for conical tanks, funnels, or caps.\n- Construction: For estimating surface treatments like cladding or insulation.\n- Education: Clarifying geometric concepts and formulas for students and professionals.", "---", "### Summary", "- The lateral surface area of a cone is calculated using ( \pi r l ).\n- With ( r = 4\ \ ext{cm} ) and ( l = 5\ \ ext{cm} ), the area is ( 20\pi\ \ ext{cm}^2 ).\n- This precise value ensures accuracy in design, budgeting, and problem-solving.", "Whether you're solving a textbook problem or tackling a project requiring geometric precision, mastering how to find the lateral surface area of a cone strengthens your spatial reasoning and practical math skills.", "---", "Key Takeaway:\nFor a cone with base radius 4 cm and slant height 5 cm, the lateral surface area is ( \boxed{20\pi\ \ ext{cm}^2} )."]
