1. Obj. 51 Prisms and Cylinders The student is able to (I can): Calculate the surface area and volume of prisms and cylinders

2. right prism oblique prism altitude A prism whose faces are all rectangles. A prism whose faces are not rectangles. A perpendicular segment joining the planes of the bases (the height). 3. Lets consider a deck of cards. If a deck is stacked neatly, it resembles a right rectangular prism. The volume of the prism is V = Bh, where B is the area of one card, and h is the height of the deck. If we shift the deck so that it becomes an oblique prism, does it have the same number of cards? 4. For any prism, whether right or oblique, the volume is V = Bh where h is the altitude, not the length of the lateral edge. 5. Likewise, for cylinders, it doesnt matter whether the cylinder is right or oblique, the volume is V = Bh = r2h 6. Examples Find the volume of each figure: 1. 2. 10 ft. 8 ft. 3 m 19 m ( )2 2 B 3 9 m= = 3 V (9 )(19) 171 m= = ( ) 1 5 B 50 172.05 2 tan36 = = V = (172)(8) = 1376 ft3 7. The surface area is the total area of all faces and curved surfaces of a three- dimensional figure. The lateral area of a prism is the sum of the areas of the lateral faces. Lets look at a net for a hexagonal prism: What shape do the lateral faces make? (a rectangle) 8. If each side of the hexagon is 1 in., what is the perimeter of the hexagon? What is the length of the base of the big rectangle? 6 in. 6 in. 9. This relationship leads to the formula for the lateral area of a prism: L = Ph where P is the perimeter and h is the height of the prism. For the total surface area, add the areas of the two bases: S = L + 2B 10. We know that a net of a cylinder looks like: The length of the lateral surface is the circumference of the circle, so the formula changes to: L = Ch where C = d or 2r and the formula for the total area is now: S = L + 2r2 11. Examples Find the lateral and total surface area of each. 1. 2. 10 cm 14 cm 4"3" 8" 5" P = 3+4+5 = 12 in. B = (3)(4) = 6 in2 L = (12)(8) = 96 in2 S = 96 + 2(6) = 108 in2 C = 10 cm B = 52 = 25 cm2 L = (10)(14) = 140 cm2 S = 140 + 2(25) = 190 cm2