FiveMinute Check over Lesson 12 2 CCSS ThenNow
- Slides: 30
Five-Minute Check (over Lesson 12– 2) CCSS Then/Now New Vocabulary Key Concept: Lateral Area of a Regular Pyramid Example 1: Lateral Area of a Regular Pyramid Key Concept: Surface Area of a Regular Pyramid Example 2: Surface Area of a Square Pyramid Example 3: Surface Area of a Regular Pyramid Key Concept: Lateral and Surface Area of a Cone Example 4: Real-World Example: Lateral Area of a Cone Example 5: Surface Area of a Cone Concept Summary: Lateral and Surface Areas of Solids
Over Lesson 12– 2 Find the lateral area of the cylinder. A. 65. 3 ft 2 B. 80. 2 ft 2 C. 122. 5 ft 2 D. 130. 7 ft 2
Over Lesson 12– 2 Find the lateral area of the prism. A. 150 in 2 B. 126 in 2 C. 108 in 2 D. 96 in 2
Over Lesson 12– 2 Find the surface area of the prism. A. 320 mm 2 B. 400 mm 2 C. 494. 2 mm 2 D. 502 mm 2
Over Lesson 12– 2 Find the surface area of the cylinder. A. 962. 5 cm 2 B. 1005. 3 cm 2 C. 1243. 6 cm 2 D. 1407. 4 cm 2
Over Lesson 12– 2 The lateral area of a prism is 476 square meters. The area of one of its bases is 25 square meters. What is the surface area of the prism? A. 426 m 2 B. 451 m 2 C. 501 m 2 D. 526 m 2
Content Standards G. MG. 1 Use geometric shapes, their measures, and their properties to describe objects (e. g. , modeling a tree trunk or a human torso as a cylinder). Mathematical Practices 1 Make sense of problems and persevere in solving them. 6 Attend to precision.
You found areas of regular polygons. • Find lateral areas and surface areas of pyramids. • Find lateral areas and surface areas of cones.
• regular pyramid • slant height • right cone • oblique cone
Lateral Area of a Regular Pyramid Find the lateral area of the square pyramid. Lateral area of a regular pyramid P = 2. 5 ● 4 or 10, ℓ = 5 Answer: The lateral area is 25 square centimeters.
Find the lateral area of the square pyramid. A. 54 in 2 B. 64 in 2 C. 108 in 2 D. 132 in 2
Surface Area of a Square Pyramid Find the surface area of the square pyramid to the nearest tenth. Step 1 Find the slant height c 2 = a 2 + b 2 Pythagorean Theorem ℓ 2 = 6 2 + 4 2 a = 6, b = 4, and c = ℓ ℓ= Simplify.
Surface Area of a Square Pyramid Step 2 Find the perimeter and area of the base. P = 4 ● 8 or 32 m Step 3 Find the surface area of the pyramid. __ S = 1 Pℓ + B 2 1 (32) = __ 2 ≈ 179. 4 A = 82 or 64 m 2 Surface area of a regular pyramid + 64 P = 32, ℓ = , B = 64 Use a calculator. Answer: The surface area of the pyramid is about 179. 4 square meters.
Find the surface area of the square pyramid to the nearest tenth. A. 96 in 2 B. 124. 3 in 2 C. 138. 5 in 2 D. 156 in 2
Surface Area of a Regular Pyramid Find the surface area of the regular pyramid. Round to the nearest tenth. Step 1 Find the perimeter of the base. P = 6 ● 10. 4 or 62. 4 cm
Surface Area of a Regular Pyramid Step 2 Find the length of the apothem and the area of the base. 360° or A central angle of the hexagon is ______ 6 60°, so the angle formed in the triangle is 30°.
Surface Area of a Regular Pyramid tan 30° = Write a trigonometric ratio to find the apothem a. a= Solve for a. a ≈ 9. 0 Use a calculator. A= Area of a regular polygon ≈ Pa (62. 4)(9. 0) Replace P with 62. 4 and a width 9. 0. ≈ 280. 8 Multiply. So, the area of the base is approximately 280. 8 cm 2.
Surface Area of a Regular Pyramid Step 3 Find the surface area of the pyramid. S= ≈ Pℓ + B Surface area of regular pyramid (62. 4)(15) + 280. 8 P = 62. 4, ℓ = 15, and B ≈ 280. 8 ≈ 748. 8 Simplify. Answer: The surface area of the pyramid is about 748. 8 cm 2.
Find the surface area of the regular pyramid. Round to the nearest tenth. A. 198 in 2 B. 228. 5 in 2 C. 255. 5 in 2 D. 316. 3 in 2
Lateral Area of a Cone ICE CREAM A sugar cone has an altitude of 8 inches and a diameter of inches. Find the lateral area of the sugar cone. If the cone has a diameter of radius then the Use the altitude and the radius to find the slant height with the Pythagorean Theorem.
Lateral Area of a Cone Step 1 Find the slant height ℓ. ℓ 2 = 82 + 1. 252 Pythagorean Theorem ℓ 2 ≈ 65. 56 Simplify. ℓ ≈ 8. 1 Step 2 Take the square root of each side. Find the lateral area L. L = rℓ Lateral area of a cone ≈ (1. 25)(8. 1) r = 1. 25 and ℓ ≈ 8. 1 ≈ 31. 8 Answer: The lateral area of the sugar cone is about 31. 8 square inches.
HATS A conical birthday hat has an altitude of 6 inches and a diameter of 4 inches. Find the lateral area of the birthday hat. A. 39. 7 in. 2 B. 43. 6 in. 2 C. 48. 2 in. 2 D. 53. 1 in. 2
Surface Area of a Cone Find the surface area of the cone. Round to the nearest tenth. Estimate: S ≈ 3 ● 1. 5 ● 3 + 3 ● 2 or 19. 5 cm 2 S = rℓ + r 2 Surface area of a cone = (1. 4)(3. 2) + (1. 4)2 r = 1. 4 and ℓ = 3. 2 ≈ 20. 2 Answer: The surface area of the cone is about 20. 2 square centimeters. This is close to the estimate, so the answer is reasonable.
Find the surface area of the cone. Round to the nearest tenth. A. 58. 2 cm 2 B. 61. 3 cm 2 C. 63. 6 cm 2 D. 70. 7 cm 2
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