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9-1C Surface Area of Cylinders and Cones

9-1C Surface Area of Cylinders and Cones. What are the parts of a cylinder? What is the formula for the lateral area of a cylinder? What is the formula for the surface area of a cylinder? What are the parts of a cone? What is the formula for the lateral area of a cone?

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9-1C Surface Area of Cylinders and Cones

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  1. 9-1C Surface Area of Cylinders and Cones What are the parts of a cylinder? What is the formula for the lateral area of a cylinder? What is the formula for the surface area of a cylinder? What are the parts of a cone? What is the formula for the lateral area of a cone? What is the formula for the surface area of a cone?

  2. Parts of a Cylinder A cylinder has two congruent circular bases in parallel planes. The axis of a cylinder is the segment that joins the centers of the bases. Right cylinder—the axis is perpendicular to the base. An altitude of a cylinder is a segment that joins the planes of the bases and is perpendicular to them. The height of a cylinder is the length of the altitude.

  3. Parts of a Cylinder radius altitude axis right cylinder

  4. Right or Oblique?

  5. Lateral Area—Can Labels What does the lateral area of a cylinder look like when it is flattened out?

  6. Lateral Area of Cylinders The lateral area of a right cylinder is the product of the circumference of its base and the height of the cylinder. LA = 2πrH Radius (r) Height (H)

  7. Surface Area of a Cylinder The surface area of a right cylinder is the sum of its lateral area and the areas of its bases. SA = 2πrH + 2πr2 Radius (r) Height (H)

  8. Find the lateral area and the surface area of the right cylinder. LA = 2πrH LA = 2π(8)(4) LA = 201.1 in2 SA = 2πrH + 2πr2 SA = 2π(8)(4) + 2π(8)2 SA = 603.2 in2 8 in 4 in

  9. Find the lateral area and the surface area of the right cylinder. C = 18π (2πr) LA = 2πrH LA = 18π(14) LA = 791.7 cm2 SA = 2πrH + 2πr2 SA = 791.7 + 2π(14)2 SA = 1300.6 cm2 14 cm

  10. Parts of a Cone vertex A cone has a vertex and a circular base. The axis of a cone is the segment from the vertex to the center of the base. In a right cone, the axis is perpendicular to the base. slant height (slant) axis height (H)

  11. Right or Oblique?

  12. Lateral Area of Cones The lateral area of a right cone is one-half the product of the circumference of its base and the slant height of the cone. LA = ½ ·2 ·π r(slant) or π (r)(slant)

  13. Surface Area of Cones The surface area of a right cone is the sum of its lateral area and the area of its base. SA = π(r)(slant) +πr2

  14. Find the lateral area of a right cone whose base radius is 4 in and slant height is 11 in. LA = π(r)(slant) LA = π(4)(11) LA = 44π≈ 138.2 in2 11 in 4 in

  15. Find the surface area of the cone. SA = π(r)(s)+πr2 SA = (4)(11)π + π(4)2 SA = 44π + 16π SA = 60π≈ 188.5 in2 11 in 4 in

  16. What are the parts of a cylinder? Raduis, altitude (height) • What is the formula for the lateral area of a cylinder? LA = 2πrH • What is the formula for the surface area of a cylinder? SA = 2πrH + 2πr2 • What are the parts of a cone? Radius, slant height • What is the formula for the lateral area of a cone? LA = π (r)(slant) • What is the formula for the surface area of a cone? SA = π(r)(slant) +πr2

  17. Assignment 9-1C Page 617, 1-10, 18-24 even NO FORMULAS WITH NUMBERS NO CREDIT

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