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Surface Areas of Cylinders

Surface Areas of Cylinders. Find the lateral areas of cylinders. Find surface areas of cylinders. Half-pipes are usually in the shape of a cylinder with flat surfaces in the center. LATERAL AREAS OF CYLINDERS.

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Surface Areas of Cylinders

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  1. Surface Areas of Cylinders • Find the lateral areas of cylinders. • Find surface areas of cylinders. Half-pipes are usually in the shape of a cylinder with flat surfaces in the center.

  2. LATERAL AREAS OF CYLINDERS The axis of a cylinder is the segment with endpoints that are centers of its circular bases. If the axis is also the altitude, then the cylinder is called a right cylinder. Otherwise, the cylinder is an oblique cylinder. Base r Axis Altitude Base Right Cylinder

  3. LATERAL AREAS OF CYLINDERS Base Base r r Axis Axis Altitude Altitude Base Base Right Cylinder Oblique Cylinder

  4. Key ConceptLateral Area of a Cylinder If a right cylinder has a lateral area of L square units, a height of h units, and the bases have radii of r units, then L = 2rh. 2r h

  5. Example 1Lateral Area of a Cylinder MANUFACTURING An office has recycling barrels for cans and paper. The barrels are cylindrical with cardboard sides and plastic lids and bases. Each barrel is 3 feet tall, and the diameter is 30 inches. How many square feet of cardboard are used to make each barrel?

  6. SURFACE AREAS OF CYLINDERS Find the lateral area and add the area of the bases.

  7. Key ConceptSurface Area of a Cylinder If a right cylinder has a lateral area of T square units, a height of h units, and the bases have radii of r units, then T = 2rh + 2r2. Area of the bases Circumference of the basesx height (lateral area) r h

  8. Example 2Surface Area of a Cylinder Find the surface area of the cylinder. 8.3 6.6

  9. Example 3Find the Missing Dimensions Find the radius of the base of a right cylinder if the surface area is 128 square centimeters and the height is 12 centimeters. T = 2rh + 2r2 128 = 2r(12) + 2r2 r 12

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