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**Standardized Test Practice**

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

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**Standardized Test Practice**

EXAMPLE 3 Standardized Test Practice 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. The correct answer is B. ANSWER

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

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**Find the lateral area of a cone**

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

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GUIDED PRACTICE for Examples 3 and 4 3. Find the lateral area of the right cone shown. SOLUTION To find the slant height l use the Pythagorean theorem l2 = 202 = 152 ,so l = 25 yd Find the lateral area

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**The lateral area of the right cone is 1178 yd2 ANSWER**

GUIDED PRACTICE for Examples 3 and 4 Lateral area = πrl Write formula. = π(15)(25) Substitute known values. ≈ Simplify and use a calculator. The lateral area of the right cone is 1178 yd2 ANSWER

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**4. Find the surface area of the right cone shown.**

GUIDED PRACTICE for Examples 3 and 4 4. Find the surface area of the right cone shown. SOLUTION S = πr2 + πrl Formula for surface area of a right cone = π(15)+ π(15)(25) Substitute. = 1885 Simplify. The surface area of the right cone is 1885yd2 ANSWER

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