FiveMinute Check over Lesson 12 2 CCSS ThenNow

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Five-Minute Check (over Lesson 12– 2) CCSS Then/Now New Vocabulary Key Concept: Lateral Area

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

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

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

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

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.

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

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

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

• 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 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

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

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

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

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.

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

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

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

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.

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

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

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

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

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.

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