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Surface Area & Volume

Lesson 15. Surface Area & Volume. Surface Area of Cones. Warm-Up. Write the surface area formula for each solid. Prism Cylinder Pyramid Find the surface area of each solid. Use 3.14 for . a. b. 2(LW + WH + LH). 2 π r h + 2 π r 2.

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Surface Area & Volume

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  1. Lesson 15 Surface Area & Volume Surface Area of Cones

  2. Warm-Up Write the surface area formula for each solid. • Prism • Cylinder • Pyramid • Find the surface area of each solid. Use 3.14 for . a. b. 2(LW + WH + LH) 2 πr h + 2 πr2 Lateral Area + Base Area

  3. Surface Area of Cones Target: Calculate the surface area of cones.

  4. Lateral Surface Area of a Cone The lateral area (LA) of a cone is equal to one-half the circumference (C) of the base times the slant height (l) of the cone. LA = Cl = πrl

  5. Total Surface Area of a Cone The surface area of a cone is equal to the sum of the lateral area (LA) and the area of the base (B). SA = LA + B SA = πrl + πr2

  6. Example 1 Jenny serves snow cones by putting flavored ice in a paper cone-shaped cup. Find the lateral area of the snow cone cup. Use 3.14 for π. • Write the formula. LA = πrl • Substitute known values. LA ≈ (3.14)(8)(10) • Multiply. LA ≈ 251.2 • The lateral area of the snow cone cup is 251.2 square centimeters.

  7. Example 2 Find the surface area of the cone. Use 3.14 for π. • Find the length of the radius. 12 ÷ 2 = 6 • Find the area of the base. πr2 ≈ (3.14)(6)2 ≈ 113.04 • Write the formula. SA = πrl + B • Substitute values. SA ≈ (3.14)(6)(9) + (113.04) • Multiply, then add. SA ≈ 169.56 + 113.04 ≈ 282. 6 • The surface area is approximately 282.6 in2.

  8. Exit Problems • The slant height of a cone is 4 feet. The radius of the cone is 3 feet. Use 3.14 for . • Find the lateral area of the cone. • Find the surface area of the cone. • The lateral area of the cone is 541.65 mm². Find the length of the radius. Use 3.14 for π.

  9. Communication Prompt • How is lateral area calculated for a prism, cylinder, pyramid and cone? • What is similar about finding the surface area of a cone and a pyramid?

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