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Lateral and Surface Area of Pyramids and Cones

Learn how to find the lateral and surface areas of pyramids and cones with helpful examples and real-world applications.

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Lateral and Surface Area of Pyramids and Cones

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 12–6) Then/Now New Vocabulary Key Concept: Lateral and Surface Area of Pyramids Example 1: Surface Area of a Pyramid Example 2: Real-World Example: Lateral Area of a Pyramid Key Concept: Lateral and Surface Area of Cones Example 3: Surface Area of a Cone Lesson Menu

  3. Find the lateral area of the figure. A. 26,384.5 mm2 B. 28,274.3 mm2 C. 40,997.8 mm2 D. 41,002.3 mm2 5-Minute Check 1

  4. Find the surface area of the figure. A. 4.7 yd2 B. 4.9 yd2 C. 5.1 yd2 D. 5.3 yd2 5-Minute Check 2

  5. Find the surface area of a cylinder with a diameter of 12 cm and a height of 29 cm. A. 1082.5 cm2 B. 1093.3 cm2 C. 1111.3 cm2 D. 1319.5 cm2 5-Minute Check 3

  6. A cylinder silo has a lateral area of 924.5 m2. The silo has a diameter of 10 meters. What is the height? A. 29.4 m B. 30.7 m C. 31.6 m D. 32.3 m 5-Minute Check 4

  7. Edwin has two cylindrical ottomans. He wants to place slipcovers over them so that fabric would cover the top and sides, but not the bottom. How much fabric is needed to cover both ottomans? A. 6,170 in2 B. 4,361 in2 C. 1,809 in2 D. 1,357 in2 5-Minute Check 5

  8. You have already found the surface areas of prisms and cylinders. (Lessons 12–5 and 12–6) • Find lateral areas and surface areas of pyramids. • Find lateral areas and surface areas of cones. Then/Now

  9. regular pyramid • slant height Vocabulary

  10. Concept A

  11. Surface Area of a Pyramid Find the lateral and total surface area of the square pyramid. First find the lateral area. The lateral area of the pyramid is made up of four triangles. Write the formula. Replace P with 8 • 4 and ℓ with 8.9 Simplify. Example 1

  12. Surface Area of a Pyramid Then find the surface area. The base of the pyramid is a square. S = L + B Write the formula. = L + s2 The area of a square is s2. = 142.4 + 82 Substitution = 206.4 ft2 Simplify. Answer: The lateral area of the square pyramid is 142.4 square feet. The surface area of the square pyramid is 206.4 square feet. Example 1

  13. Find the surface area of the square pyramid. A. 16.5 m2 B. 33 m2 C. 42 m2 D. 75 m2 Example 1

  14. Write the formula for lateral area. Replace P with 3.4 ● 4 and ℓ with 2. Lateral Area of a Pyramid CANOPIESA canopy is in the shape of a square pyramid. If the length of each side is 3.4 meters and the slant height is 2 meters, how much canvas is needed for the canopy? Find the lateral area only, since there is no bottom to the canopy. Example 2

  15. Lateral Area of a Pyramid L = 13.6 m2 Simplify. Answer: So, 13.6 square meters of canvas was used to cover the canopy. Example 2

  16. TENTA tent is in the shape of a square pyramid that is 8 feet on each side. The slant height is 10 feet.Find the lateral area of the tent. A. 320 ft2 B. 224 ft2 C. 160 ft2 D. 80 ft2 Example 2

  17. Concept B

  18. Surface Area of a Cone Find the lateral and surface areas of the cone. Round to the nearest tenth. Find the lateral area. L = πrℓ Lateral area of a cone = π(3.5)(10) Replace r with 3.5 andℓ with 10. ≈ 110.0 ft2 Simplify. Example 3

  19. Surface Area of a Cone Find the surface area. S = L + πr2 Surface area of a cone ≈ 110 + π(3.5)2 Replace L with 110 and r with 3.5. ≈ 148.5 ft2 Simplify. Answer: The lateral area is about 110.0 square feet and the surface area is about 148.5 square feet. Example 3

  20. Find the surface area of the cone. Round to the nearest tenth. A. 376.1 cm2 B. 587.4 cm2 C. 963.5 cm2 D. 1028.0 cm2 Example 3 CYP

  21. End of the Lesson

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