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OBJECTIVE AFTER STUDYING THIS SECTION, YOU WILL BE ABLE TO FIND THE SURFACE AREAS OF CIRCULAR SOLIDS 12.3 Surface Areas of Circular Solids

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Cylinders A cylinder resembles a prism in having two congruent parallel bases. The bases are circles. If we look at the net of a cylinder, we can see two circles and a rectangle. The circumference of the circle is the length of the rectangle and the height is the width.

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Theorem The lateral area of a cylinder is equal to the product of the height and the circumference of the base where C is the circumference of the base, h is the height of the cylinder, and r is the radius of the base.

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Definition The total area of a cylinder is the sum of the cylinder’s lateral area and the areas of the two bases.

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Cone A cone resembles a pyramid but its base is a circle. The slant height and the lateral edge are the same in a cone. Slant height (italicized l) height radius

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Theorem The lateral area of a cone is equal to one-half the product of the slant height and the circumference of the base where C is the circumference of the base, l is the slant height, and r is the radius of the base.

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Definition The total area of a cone is the sum of the lateral area and the area of the base.

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Sphere A sphere is a special figure with a special surface-area formula. (A sphere has no lateral edges and no lateral area).

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Postulate where r is the sphere’s radius

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Example 1 Find the total area of the figure 5 6

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Example 2 Find the total area of the figure 5 6

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Example 3 Find the total area of the figure 5

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Summary Explain in your own words how to find the surface area of a cylinder? Homework: worksheet

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