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Surface Areas of Prisms and Cylinders

Use the prism below for Exercises 1 and 2. 1. Use a net to find the surface area. 2. Use a formula to find the surface area. 3. The height of a prism is 5 cm. Its rectangular bases have 3-cm and 9-cm sides. Find its surface area.

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Surface Areas of Prisms and Cylinders

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  1. Use the prism below for Exercises 1 and 2. 1. Use a net to find the surface area. 2. Use a formula to find the surface area. 3. The height of a prism is 5 cm. Its rectangular bases have 3-cm and 9-cm sides. Find its surface area. 4. The radius of the base of a cylinder is 16 in., and its height is 4 in. Find its surface area in terms of . 5. A contractor paints all but the bases of a 28-ft high cylindrical water tank. The diameter of the base is 22 ft. How many square feet are painted? Round to the nearest hundred. S.A. = 216 ft2 640 in.2 Surface Areas of Prisms and Cylinders Lesson 11-2 Lesson Quiz S.A. = L.A. + 2B = 168 + 48 = 216; 216 ft2 174 cm2 1900 ft2 11-3

  2. Surface Areas of Pyramids and Cones Lesson 11-3 Check Skills You’ll Need (For help, go to Lesson 8-1.) Find the length of the hypotenuse in simplest radical form. 1.2.3. Check Skills You’ll Need 11-3

  3. Surface Areas of Pyramids and Cones Lesson 11-3 Notes A pyramid is a polyhedron in which one face (the base) can be any polygon and the other faces (the lateral faces) are triangles that meet at a common vertex (called the vertex of the pyramid). 11-3

  4. Surface Areas of Pyramids and Cones Lesson 11-3 Notes The vertex of a pyramidis the point opposite the base of the pyramid. The base of a regular pyramidis a regular polygon, and the lateral faces are congruent isosceles triangles. The slant height of a regular pyramidis the distance from the vertex to the midpoint of an edge of the base. The altitude of a pyramidis the perpendicular segment from the vertex to the plane of the base. 11-3

  5. Surface Areas of Pyramids and Cones Lesson 11-3 Notes The lateral faces of a regular pyramid can be arranged to cover half of a rectangle with a height equal to the slant height of the pyramid. The width of the rectangle is equal to the base perimeter of the pyramid. 11-3

  6. Surface Areas of Pyramids and Cones Lesson 11-3 Notes 11-3

  7. You are given = 12 ft and you found that p= 30, so you can find the lateral area. 1 2 L.A. = p Use the formula for lateral area of a pyramid. 1 2 = (30)(12)Substitute. Surface Areas of Pyramids and Cones Lesson 11-3 Additional Examples Finding Surface Area of a Pyramid Find the surface area of a square pyramid with base edges 7.5 ft and slant height 12 ft. The perimeter p of the square base is 4 X 7.5 ft, or 30 ft. = 180Simplify. 11-3

  8. Find the area of the square base. S.A. = L.A. BUse the formula for surface area of a pyramid. = 180  56.25Substitute. Surface Areas of Pyramids and Cones Lesson 11-3 Additional Examples (continued) Because the base is a square with side length 7.5 ft, Bs2 7.52 56.25. = 236.25Simplify. The surface area of the square pyramid is 236.25 ft 2. Quick Check 11-3

  9. 1 2 Use the formula L.A. =p to find the lateral area of the pyramid. The altitude of the pyramid, apothem of the base, and altitude of a lateral face form a right triangle, so you can use the Pythagorean Theorem to find the slant height . = 202 + (4 3)2 = 400 + 48 = 448 Surface Areas of Pyramids and Cones Lesson 11-3 Additional Examples Finding Lateral Area of a Pyramid Find the lateral area of the hexagonal pyramid below. Round your answer to the nearest whole number. 11-3

  10. 1 2 L.A. =pUse the formula for lateral area. 1 2 = (48)( 448) Substitute. 507.98425 Use a calculator. Surface Areas of Pyramids and Cones Lesson 11-3 Additional Examples (continued) The lateral area of the hexagonal pyramid is about 508 m2. Quick Check 11-3

  11. Surface Areas of Pyramids and Cones Lesson 11-3 Notes A cone is formed by a circular base and a curved surface that connects the base to a vertex. The vertex of a coneis the point opposite the base. The axis of a coneis the segment with endpoints at the vertex and the center of the base. The axis of a right coneis perpendicular to the base. The axis of an oblique coneis not perpendicular to the base. 11-3

  12. Surface Areas of Pyramids and Cones Lesson 11-3 Notes The slant height of a right coneis the distance from the vertex of a right cone to a point on the edge of the base. The altitude of a coneis a perpendicular segment from the vertex of the cone to the plane of the base. 11-3

  13. Surface Areas of Pyramids and Cones Lesson 11-3 Notes 11-3

  14. = r+r 2Substitute the formulas for L.A. and B. = (5)(13) + (5)2Substitute. = 65 + 25Simplify. = 90 The surface area of the cone is 90 in.2. Surface Areas of Pyramids and Cones Lesson 11-3 Additional Examples Finding Surface Area of a Cone Find the surface area of the cone in terms of . S.A. = L.A.+ BUse the formula for surface area of a cone. Quick Check 11-3

  15. Use the formula L.A. =r to find the lateral area of the cone. The altitude of the cone, radius of the base, and slant height form a right triangle. Use the Pythagorean Theorem to find the slant height . = 0.52  1.52 = 0.25  2.25 = 2.5 Surface Areas of Pyramids and Cones Lesson 11-3 Additional Examples Real-World Connection Leandre uses paper cones to cover her plants in the early spring. The diameter of each cone is 1 ft, and its height is 1.5 ft. How much paper is in the cone? Round your answer to the nearest tenth. The cone’s diameter is 1 ft, so its radius r is 0.5 ft. 11-3

  16. L.A. =r Use the formula for lateral area of a cone. = (0.5) 2.5 Substitute 0.5 for r and 2.5 for . 2.4836471 Use a calculator. Surface Areas of Pyramids and Cones Lesson 11-3 Additional Examples (continued) Find the lateral area. The lateral area of the cone is about 2.5 ft.2 Quick Check 11-3

  17. Textbook

  18. 1. Find the slant height of a square pyramid with base edges 12 cm and altitude 8 cm. 2. Find the lateral area of the regular square pyramid to the right. 3. Find the surface area of the pyramid to the right whose base is a regular hexagon. Round to the nearest whole number. 4. Find the surface area of a cone with radius 8 cm and slant height 17 cm in terms of . 5. The roof of a building is shaped like a cone with diameter 40 ft and height 20 ft. Find the area of the roof. Round to the nearest whole number. 200 cm2 Surface Areas of Pyramids and Cones Lesson 11-3 Lesson Quiz 10 cm 56 in.2 1517 ft2 1777 ft2 11-3

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