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12.4 Surface Areas of Cylinders

12.4 Surface Areas of Cylinders. Objectives. Find lateral areas of cylinders Find surface areas of cylinders. Lateral Areas of Cylinders. The axis of the cylinder is the segment with endpoints that are centers of the circular bases.

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12.4 Surface Areas of Cylinders

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  1. 12.4 Surface Areas of Cylinders

  2. Objectives • Find lateral areas of cylinders • Find surface areas of cylinders

  3. Lateral Areas of Cylinders • The axis of the cylinder is the segment with endpoints that are centers of the circular bases. • If the axis is also the altitude, then the cylinder is a right cylinder. • Otherwise, the cylinder is an oblique cylinder. Base Altitude Axis Base

  4. h 2πr r Net of a Cylinder • The net of a cylinder is composed of two congruent circles and a rectangle. The area of this rectangle is the lateral area. The length of the rectangle is the same as the circumference of the base, 2πr. So, the lateral area of a right cylinder is 2πrh.

  5. Lateral 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=2πrh 2πr h

  6. Example 1 • A zoo has recycling barrels for storing animal feed. The barrels are cylindrical with cardboard sides and plastic lids and bases. Each barrel is 4 feet tall, and the diameter is 60 inches. How many square feet of cardboard are used to make each barrel?

  7. The cardboard section of the barrel represents the lateral area of the cylinder. If the diameter is 60, then the radius is 30 inches. The height is 4 feet, or 48 inches.L=2πrh =2π(30)(48) =9047.8 Each barrel uses about 9048 square inches of cardboard. 144 sq. inches = 1 sq. ft. there are about 9048/144 or 62.8 sq. ft. per barrel.

  8. Surface Areas of Cylinders • To find the surface area of a cylinder, first find the lateral area and then add the areas of the bases. This leads to the formula for the surface area of a right cylinder.

  9. Surface Area of a Cylinder • If a right cylinder has a surface area of T sq. units, a height of h units, and the bases have radii of r units, then…. • T= 2πrh + 2πr 2 r h

  10. 5.3 ft 7.5ft Surface Area of a Cylinder • Find the surface area of the cylinder.

  11. 5.3 ft 7.5ft Cont… 2 • T= 2πrh + 2πr • = 2π(5.3)(7.5) + 2π(5.3) • = 426.3 sq ft 2

  12. Find Missing Dimensions • Find the radius of the base of a cylindrical cup if the surface area is 57πsq inches and the height is 6 inches.

  13. Cont… 2 • T=2πrh + 2πr • 57π = 2π(6)r + 2πr • 57π =12πr +2πr • 28.5 = 6r + r (Divide each side by 2π) • 0 = r + 6r – 28.5 • r = -6 +√6 -4(1)(-28.5) / 2(1) • r =3.1 • Radius of base = 3.1inches 2 2 2 2 - 2

  14. Assignment • Pg 657 #9-20, 24, 25

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