Main Idea and New Vocabulary Key Concept: Surface Area of a Pyramid

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Find the lateral and total surface areas of pyramids.

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Presentation transcript:

Main Idea and New Vocabulary Key Concept: Surface Area of a Pyramid Example 1: Surface Areas of a Pyramid Example 2: Real-World Example Key Concept: Surface Area of a Cone Example 3: Surface Area of a Cone Lesson Menu

Find the lateral and total surface areas of pyramids and cones. regular pyramid slant height Main Idea/Vocabulary

Key Concept

Surface Areas of a Pyramid Find the lateral and total surface areas of the triangular pyramid. L.A. = Pℓ S.A. = L.A. + B S.A. = 60 + 10.8 S.A. = 70.8 L.A. = • 15 • 8 L.A. = 60 Answer: The lateral and total surface areas are 60 and 70.8 square inches. Example 1

Find the lateral and total surface areas of the triangular pyramid. A. 20 m2; 26 m2 B. 30 m2; 36 m2 C. 30 m2; 46 m2 D. 60 m2; 66 m2 Example 1 CYP

TOYS A toy block has the shape of a regular pyramid with a square base TOYS A toy block has the shape of a regular pyramid with a square base. The manufacturer wants to paint the lateral surface green. How many square centimeters will be painted green? Example 2

L.A. = Pℓ Lateral surface area of a pyramid L.A. = • 28 • 8 P = 7(4) or 28 and ℓ = 8 L.A. = 112 Simplify. Answer: So, 112 square centimeters of the toy will be painted green. Example 2

ORNAMENTS A garden ornament is a square pyramid with an 11-inch-long base and a 24-inch slant height. Find the ornament’s lateral surface area. A. 352 in2 B. 528 in2 C. 649 in2 D. 1,056 in2 Example 2 CYP

Key Concept 3

L.A. = rℓ Lateral area of a cone Surface Area of a Cone Find the lateral and total surface areas of the cone. Round to the nearest tenth. L.A. = rℓ Lateral area of a cone L.A. =  • 6 • 13.4 Replace r with 6 and ℓ with 13.4. L.A.  252.6 Simplify. S.A. = L.A. + r2 Surface area of a cone S.A. = 252.6 +  • 62 Replace L.A. with 252.6 and r with 6. S.A.  365.7 Simplify. Example 3

Surface Area of a Cone Answer: The lateral and total surface areas of the cone are about 252.6 and 365.7 square meters. Example 3

Find the lateral and total surface areas of the cone Find the lateral and total surface areas of the cone. Round to the nearest tenth. A. 84.8 cm2; 113.1 cm2 B. 84.8 cm2; 148.4 cm2 C. 169.6 cm2; 197.9 cm2 D. 169.6 cm2; 233.3 cm2 Example 3 CYP