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12-4

12-4. Surface Area of Cylinders. Vocabulary. Axis - the segment with endpoints that are centers of the circular bases Right cylinder - a cylinder with an axis that is also an altitude Oblique cylinder - a cylinder with bases that are not aligned one directly on top of one another.

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12-4

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  1. 12-4 Surface Area of Cylinders

  2. Vocabulary • Axis- the segment with endpoints that are centers of the circular bases • Right cylinder- a cylinder with an axis that is also an altitude • Oblique cylinder- a cylinder with bases that are not aligned one directly on top of one another

  3. Lateral Area of a Cylinder • Lateral area- the area of the rectangle • The net of a cylinder is composed of two congruent circles and a rectangle. • The length of the rectangle is the same as the circumference of the base, 2 r. • The lateral area of a right cylinder is L=2 rh.

  4. Example 1- Lateral Area of a Cylinder • MANUFACTURINGAn office has recycling barrels for cans and paper. The barrels are cylindrical with cardboard sides and plastic lids and bases. Each barrel is three feet tall, and the diameter is thirty inches. How many square feet of cardboard are used to make each barrel. • The cardboard section of the barrel represents the lateral area of the cylinder. If the diameter of the lid is thirty inches, then the radius is fifteen inches. The height is three feet or thirty-six inches. Use the formula to find the lateral area.

  5. L=2 rh • =2 (15)(36) • =about 3392.9 • Lateral area of a cylinder • r=15, h=36 • Use a calculator Each barrel uses approximately 3393 square inches of cardboard. Because 144 square inches equal one square foot, there are 3393 144 or about 23.6 square feet of cardboard per barrel.

  6. Surface Area of a Cylinder • To find the surface area of a cylinder, first find the lateral area and then add the bases. T=2 rh+2 r

  7. Example 2- Surface Area of a Cylinder • Find the surface area of the cylinder. • The radius of the base is 8.3 ft. The height of the cylinder is 6.6 ft. Substitute these values in the formula to find the surface area. T=2 rh+2 r =2 (8.3)(6.6)+2 (8.3 ) =about 777.0 Surface area of a cylinder r=8.3, h=6.6 Use a calculator 8.3 ft. The surface area is approximately 777.0 square feet. 6.6 ft.

  8. Assignment • Pg.657 #9-22 all

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