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Surface Areas of Prisms & Cylinders

Surface Areas of Prisms & Cylinders. Section 11-2. Objectives. To find the surface area of a prism To find the surface area of a cylinder. All About Prisms. Prism - a polyhedron w/ exactly 2 congruent, parallel faces, called bases.

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Surface Areas of Prisms & Cylinders

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  1. Surface Areas of Prisms & Cylinders Section 11-2

  2. Objectives • To find the surface area of a prism • To find the surface area of a cylinder

  3. 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

  4. 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

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

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

  7. Formulas

  8. 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 Draw the base. Use 30°-60°-90° triangles to find the apothem. Find the surface area of a 10-cm high right prism with triangular bases having 18-cm edges. Round to the nearest whole number. The triangle has sides of length 18 cm, so p = 3 • 18 cm, or 54 cm.

  9. 9 = 3 alonger leg  3  shorter leg 9 3 3 3 3 a== = 3 3Rationalize the denominator. = (54)(10) + 2(81 3 ) Substitute 1 2 1 2 B=ap = 3354 = 81 3 S.A. =L.A. + 2BUse the formula for surface area. = 540 + 162 3 The area of each base of the prism is 81 3 cm2. =ph + 2B 820.59223Use a calculator. 9 3 (continued) Rounded to the nearest whole number, the surface area is 821 cm2.

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

  11. 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

  12. =2rh + 2( r 2) Substitute the formula for lateral area of a cylinder and area of a circle. = 2 (6)(9) + 2 (62) Substitute 6 for r and 9 for h. = 108 + 72 Simplify. = 180 The surface area of the cylinder is 180 ft2. 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. + 2BUse the formula for surface area of a cylinder.

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

  14. Cornmeal Container Barley Container S.A. =L.A. + 2B Use the formula for surface area of a cylinder. S.A. =L.A. + 2B Substitute the formulas for lateral area of a cylinder and area of a circle. =2rh + 2 r 2 =2rh + 2 r 2 d 2 Find the surface area of each container. Remember that r= . 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?

  15. =2rh + 2 r 2 =2rh + 2 r 2 Substitute for r and h. = 2 (2)(6) + 2(22) = 2 (3)(4) + 2(32) Simplify. = 24 + 8 = 24 + 18 = 32 = 42 Because 42 in.2 32 in.2, the barley container has the greater surface area. (continued) Cornmeal Container Barley Container S.A. =L.A. + 2B Use the formula for surface area of a cylinder. S.A. =L.A. + 2B Substitute the formulas for lateral area of a cylinder and area of a circle.

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