1. 12.2 Surface Area of Prisms and Cylinders Hubarth Geometry

2. 8in 3in 5in Find the surface area of the rectangular prism. The surface area of a polyhedron is the sum of the areas of its faces. Ex 1 Find The Surface Area of the Prism Solution Add the area of all the rectangles that form the faces of the prism. Congruent FacesDimensionsArea of Face Left face and right face3in by 5in3 X 5= 15in 2 Front face and back face8in by 5in8 X 5 = 40in 2 Top face and bottom face8in by 3in8 X 3 = 24in 2 Area= 158 square inches

3. Lateral Faces and Area The lateral faces of a prism are the faces of the prism that are not bases. Lateral area is the sum of the areas of the lateral faces. Theorem 12.2 Surface Area of a Right Prism Words Surface area= 2(area of base) + (perimeter of base)(height) Symbols S=2B + Ph h l w

4. Ex 2 Find Surface Area of a Prism Find the surface area of the prism. 4m 6m 5m 7m 3m Solution

5. A cylinder is a solid with two congruent bases that lie in Parallel planes. The lateral area of a cylinder is the area of the curved surface.. base Radius r Height h Lateral surface

6. = + h r r r r h Surface = 2(area of base) + lateral area area = +

7. Theorem 12.3 Surface Area of a Right Cylinder r h

8. Ex 3. Find Surface Area of a Cylinder Find the surface area of the cylinder. Round your answer to the nearest whole number. 4ft 3ft Solution

9. Ex 3 Find the Height of a Cylinder Substitute known values in the formula for the surface area of a right cylinder and solve for the height h. Find the height of the right cylinder shown, which has a surface area of 157.08 square meters. S = 2πr 2 + 2πrh 157.08 = 2π(2.5) 2 + 2π(2.5)h 157.08 = 12.5π + 5πh 157.08 – 12.5π = 5πh 117.81 ≈ 5πh 7.5 ≈ h

10. Practice Find the surface area of the prism. 1. 2. 3in 6in 2in 10cm 8cm 6cm 4cm 3. Find the surface area of the cylinder 10ft 12 ft