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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?

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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.

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Parts of a Cylinder right cylinder altitude axis radius

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Right or Oblique?

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

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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)

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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 + 2πr 2 Radius (r) Height (H)

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

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

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Parts of a Cone 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. vertex axis height (H) slant height (slant)

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Right or Oblique?

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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)

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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) +πr 2

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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 in 2 4 in 11 in

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

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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 + 2πr 2 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) +πr 2

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

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