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Understanding Right Cone Surface Area and Lateral Area Using Pythagorean Theorem

This guide covers the calculation of slant height, lateral area, and surface area of right cones using the Pythagorean Theorem and associated formulas. It includes step-by-step examples, such as finding slant height, lateral area for traffic cones, and surface area calculations. Key formulas are provided, including the lateral area ( L = pi r l ) and surface area ( S = pi r^2 + pi r l ). The examples demonstrate how to apply these concepts to practical problems, making it easier for students to grasp important geometric principles.

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Understanding Right Cone Surface Area and Lateral Area Using Pythagorean Theorem

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  1. Standardized Test Practice EXAMPLE 3 SOLUTION To find the slant height l of the right cone, use the Pythagorean Theorem. l2 = h2+ r 2 Write formula. l2 = 82 + 62 Substitute. l = 10 Find positive square root.

  2. ANSWER The correct answer is B. Standardized Test Practice EXAMPLE 3 Use the formula for the surface area of a right cone. S = πr2 + πrl Formula for surface area of a right cone = π(62) + π(6)(10) Substitute. = 96π Simplify.

  3. The traffic cone can be approximated by a right cone with radius 5.7 inches and height 18inches. Find the approximate lateral area of the traffic cone. Find the lateral area of a cone EXAMPLE 4 TRAFFIC CONE SOLUTION To find the slant height l,use the Pythagorean Theorem. l2 = 182 + (5.7)2, sol≈ 18.9 inches.

  4. ANSWER The lateral area of the traffic cone is about 338.4 square inches. Find the lateral area of a cone EXAMPLE 4 Find the lateral area. Lateral area = πrl Write formula. = π(5.7)(18.9) Substitute known values. ≈ 338.4 Simplify and use a calculator.

  5. 3. Find the lateral area of the right cone shown. ANSWER The lateral area of the right cone is1178yd2 for Examples 3 and 4 GUIDED PRACTICE

  6. 4. Find the surface area of the right cone shown. ANSWER The surface area of the right cone is1885yd2 for Examples 3 and 4 GUIDED PRACTICE

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