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**Surface Areas of Prisms & Cylinders**

Section 11-2

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**Objectives To find the surface area of a prism**

To find the surface area of a cylinder

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All About Prisms Prism - a polyhedron w/ exactly 2 congruent, parallel faces, called bases. Lateral faces - the faces that are not bases in a polyhedron Named by the shape of its bases Altitude - perpendicular segment that joins the planes of the bases Height (h) - length of the altitude

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**Vocab Ctd. Lateral area - the sum of the areas of the lateral faces**

Surface area - the sum of the lateral area and area of the two bases

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**Use a net to find the surface area of the cube.**

Draw a net for the cube. Find the area of one face. 112 = 121 The area of each face is 121 in.2. Surface Area = sum of areas of lateral faces + area of bases = ( ) + ( ) = 6 • 121 = 726 Because there are six identical faces, the surface area is 726 in.2.

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You try Use a net to find the S.A. of the triangular prism

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Formulas

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**Use the formula L.A. = ph to find the lateral area and the formula **

Find the surface area of a 10-cm high right prism with triangular bases having 18-cm edges. Round to the nearest whole number. Use the formula L.A. = ph to find the lateral area and the formula S.A. = L.A. + 2B to find the surface area of the prism. The area B of the base is ap, where a is the apothem and p is the perimeter. 1 2 The triangle has sides of length 18 cm, so p = 3 • 18 cm, or 54 cm. Draw the base. Use 30°-60°-90° triangles to find the apothem.

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**9 = 3 a longer leg 3 shorter leg**

(continued) 9 = a longer leg shorter leg 9 3 3 9 a = = = Rationalize the denominator. B = ap = 54 = 1 2 The area of each base of the prism is cm2. S.A. = L.A B Use the formula for surface area. = ph + 2B = (54)(10) + 2( ) Substitute = Use a calculator. Rounded to the nearest whole number, the surface area is 821 cm2.

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You try Use formulas to find L.A. & S.A. of the prism

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**All About Cylinders Has 2 congruent parallel bases, which are circles.**

Altitude - perpendicular segment that joins the planes of the bases Height - length of the altitude L.A. - area of resulting rectangle that can be formed by unrolling the cylinder S.A. - sum of the lateral area & area of bases

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**The radius of the base of a cylinder is 6 ft, and its height is 9 ft**

The radius of the base of a cylinder is 6 ft, and its height is 9 ft. Find its surface area in terms of . S.A. = L.A B Use the formula for surface area of a cylinder. = rh + 2( r 2) Substitute the formula for lateral area of a cylinder and area of a circle. = (6)(9) (62) Substitute 6 for r and 9 for h. = Simplify. = 180 The surface area of the cylinder is ft2.

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You try Find the S.A. of a cylinder with a height of 10cm and radius of 10cm in terms of pi. 400cm2

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**Use the formula for surface area of a cylinder.**

A company sells cornmeal and barley in cylindrical containers. The diameter of the base of the 6-in. high cornmeal container is 4 in. The diameter of the base of the 4-in. high barley container is 6 in. Which container has the greater surface area? Find the surface area of each container. Remember that r = . d 2 S.A. = L.A B Cornmeal Container Barley Container Use the formula for surface area of a cylinder. = rh r 2 Substitute the formulas for lateral area of a cylinder and area of a circle.

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**surface area of a cylinder.**

(continued) Cornmeal Container Barley Container S.A. = L.A B Use the formula for surface area of a cylinder. S.A. = L.A B = rh r 2 Substitute the formulas for lateral area of a cylinder and area of a circle. = rh r 2 = (2)(6) (22 ) = (3)(4) (32 ) Substitute for r and h. = = Simplify. = 32 = 42 Because in.2 in.2, the barley container has the greater surface area.

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