Surface Area: Prisms and Cylinders (10-5) What is surface area? How do you find surface? surface area – the sum of the areas of all of the bases and faces that make a space figure (in other words, the number of square units that would cover the \ entire figure) To find the surface area, make a net of the figure, find the area of each part of The net, and add up all the areas of the net (in other words, find the total area of the net) Example: Find the surface area of the following rectangular prism using a net. 1. Draw and label a net. 2. Then, find the area of each rectangle in the net. 40 + 4- + 16- + 100 + 160 + 100 = 600 3. Add the areas. The surface area is 600 square in. (in. 2)

Find the surface area of the rectangular prism using a net. Surface Area: Prisms and Cylinders LESSON 10-5 Additional Examples Find the surface area of the rectangular prism using a net. Find the area of each rectangle in the net. Draw and label a net. 60 + 60 + 150 + 90 + 150 + 90 = 600 Add the areas. The surface area is 600 cm2.

Surface Area: Prisms and Cylinders (10-5) What is lateral area? How do you find lateral area? lateral area (L.A.) – the sum of the area of the lateral (side) faces To find the lateral area: 1. add up the areas of the side faces, or 2. Use the following formulas. Lateral Area (L.A.) Formula (prism) = perimeter of base (p) x height (h) Lateral Area (L.A.) Formula (cylinder) = Circumference of base (C) x height (h), where C = 2r L.A.(cylinder) = p(base)h L.A.(cylinder) = C(base)h = (2r)h

Surface Area: Prisms and Cylinders (10-5) How do you find surface area of a prism or cylinder using a formula? Surface Area (S.A.) = Lateral Area (L.A.) + 2 Base Areas (2B) S.A.(prism) = L.A. + 2B S.A.(cylinder) = L.A. + 2B Example: Find the surface area of the following triangular prism. Step 1: Find the lateral area. L.A. = perimeter (p) of base  height (h) = (5 + 5 + 5)  12 = = 192 Step 2: Find the surface area. S.A. = lateral area (L.A.) + 2 base areas (2B) = 192 + 2 (½ · 6 · 4) = 192 + 24 = 216 The surface area of the triangular prism is 216 square cm. (cm. 2)

Find the surface area of the rectangular prism. Surface Area: Prisms and Cylinders LESSON 10-5 Additional Examples Find the surface area of the rectangular prism. Step 1: Find the lateral area. L.A. = ph Use the formula for lateral area. = (5 + 6 + 5 + 6) 20 p = 5 + 6 + 5 + 6 and h = 20 = 440 Step 2: Find the surface area. S.A. = L.A. + 2B Use the formula for surface area = 440 + 2(5 • 6) L.A. = 440 and B = 5 • 6 = 440 + 60 = 500 The surface area of the rectangular prism is 500 in.2.

Surface Area: Prisms and Cylinders (10-5) Example: Find the surface area of the following sardine can to the nearest square centimeter. Step 1: Find the lateral area. L.A. = Circumference (C = 2r) of base x height (h) = 2r · h = 2 · 3.5 · 11.5 = 80.5   Step 2: Find the surface area. S.A. = lateral area (L.A.) + 2 base areas (2B) S.A. = L.A. + 2r2 = 80.5 + 2(3.5)2 = 80.5 + 24.5 = 105  330 The surface area of the can is 105 square cm. (cm.2 ) or about 330 square cm. (cm. 2).

Find the surface area of the cylindrical water tank. Surface Area: Prisms and Cylinders LESSON 10-5 Additional Examples Find the surface area of the cylindrical water tank. Step 1: Find the lateral area. 2 (8)(15)  240 r = 8 and h = 15 L.A. = 2 rh Use the formula for lateral area. Step 2: Find the surface area. S.A. = L.A. + 2B Use the formula for surface area. = 240 + 2(8)2 = 240 + 128 L.A. = 240p and B = p(8)2 = 368  368 (3.14) Use 3.14 for p. Round.  1,156 The surface area of the water tank is about 1,156 ft2.

3. cylindrical candle with radius 2 cm and height 16 cm 408 cm2 Surface Area: Prisms and Cylinders LESSON 10-5 Lesson Quiz Find the surface area of each figure rounded to the nearest whole unit. 1. triangular prism with base perimeter 24 cm, base area 24 cm2, and height 15 cm 2. rectangular prism with base perimeter 30 cm, base area 50 cm2, and height 150 cm 3. cylindrical candle with radius 2 cm and height 16 cm 408 cm2 4,600 cm2 about 226 cm2