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Surface Area and Volume of Cylinders

Surface Area and Volume of Cylinders. What is a Cylinder?. 3 dimensional geometric shape Has length, width, and height Circles of the same size stacked on top of each other

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Surface Area and Volume of Cylinders

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  1. Surface Area and Volume of Cylinders

  2. What is a Cylinder? • 3 dimensional geometric shape • Has length, width, and height • Circles of the same size stacked on top of each other • A cylinder is similar to a prism, but its two bases are circles, not polygons. Also, the sides of a cylinder are curved, not flat.

  3. Why are cylinders important? • Sustenance: Used to store liquids and potato chips • Shelter: Support posts in buildings are made of cylinders • Transportation and Industry: Pistons in automobile engine are small cylinders • Economics: Coins are cylinders • Sports: hockey pucks and tennis ball containers

  4. Fuel and Drums • The drums (or cylinders) are typically made of steel with a ribbed outer wall to improve rigidity and durability. They are often moved by tilting, then rolling along the base, which is designed especially for that purpose. The drums are commonly used for transporting oils and fuels, but can be used for storing various chemicals as well.

  5. Automobile Engine • The core of the engine is the cylinder, with the piston moving up and down inside the cylinder. Most cars have more than one cylinder (four, six and eight cylinders are common). In a multi-cylinder engine, the cylinders usually are arranged in one of three ways: inline, V or flat (also known as horizontally opposed or boxer), as shown in the following figures. • 4 Cylinder Inline Engine • 6 Cylinder-V Shaped • 4 Cylinder Flat

  6. Pools • Volume of pools • The amount of chemicals added is determined by the size of the pool. • To Calculate a the size of a circular or oval pool you must use the volume forumla

  7. Hockey • Originally, hockey players weren’t picky about what they used as a puck: a piece of coal, an apple, a knot of wood. Eventually, a rubber ball similar to a lacrosse ball was used. • In the 1860s, when games started to be played in Montreal’s indoor Victoria Rink, the ball broke so many windows that the fed-up arena manager grabbed it, sliced off the top and bottom and threw what was left back on the ice. The players quickly discovered that the new shape reduced bouncing and made passing easier.

  8. Cylinders • A cylinder has 2 main parts. • A rectangle and a circle – well, 2 circles really. • Put together they make a cylinder.

  9. The Soup Can Think of the Cylinder as a soup can. You have the top and bottom lid (circles) and you have the label (a rectangle – wrapped around the can). The lids and the label are related. The circumference of the lid is the same as the length of the label.

  10. Net of a Cylinder • Closed cylinder (top and bottom included) • Rectangle and two congruent circles • What relationship must exist between the rectangle and the circles? • Are other nets possible?

  11. Area of the Circles Formula for Area of Circle A=  r2 = 3.14 x 32 = 3.14 x 9 = 28.26 But there are 2 of them so 28.26 x 2 = 56.52 units squared

  12. To Find the Surface Area of a Cylinder You must find the area of the 2 circle and the area of the rectangle and add them together

  13. The Rectangle • This has 2 steps. To find the area we need base and height. Height is given (6) but the base is not as easy. • Notice that the base is the same as the distance around the circle (or the Circumference).

  14. Area of the Rectangle Formula is C =  x d = 3.14 x 6 (radius doubled) = 18.84 Now use that as your base. A = b x h = 18.84 x 6 (the height given) = 113.04 units squared

  15. Total Surface Area Now add the area of the circles and the area of the rectangle together. 56.52 + 113.04 = 169.56 units squared The total Surface Area!

  16. Formula SA = ( d x h) + 2 ( r2) Label Lids (2) Area of Rectangle Area of Circles

  17. Practice

  18. Check! SA = ( d x h) + 2 ( r2) = (3.14 x 22 x 14) + 2 (3.14 x 112) = (367.12) + 2 (3.14 x 121) = (367.12) + 2 (379.94) = (367.12) + (759.88) = 1127 cm2

  19. 11 cm 7 cm Practice

  20. Check! SA = ( d x h) + 2 ( r2) = (3.14 x 11 x 7) + 2 ( 3.14 x 5.52) = (241.78) + 2 (3.14 x 30.25) = (241.78) + 2 (3.14 x 94.99) = (241.78) + 2 (298.27) = (241.78) + (596.54) = 838.32 cm2

  21. How to calculate the volume • Find the area of the circle • Find the height V = π r2 h remember: the answer is always in cubic units in3, ft3, mi3

  22. Let's find the volume of this can of potato chips.

  23. Check! • We'll use 3.14 for pi. Then we perform the calculations like this: • That's a lot of potato chips!

  24. Hmmmm….

  25. Find the Volume…

  26. Check! • V = r2h • The radius of the cylinder is 5 m, and the height is 4.2 m • V = 3.14 · 52 · 4.2 • V =329.7

  27. Practice 13 cm - radius 7 cm - height

  28. Check! • V = r2h Start with the formula • V = 3.14 x 132 x 7 substitute what you know • = 3.14 x 169 x 7 Solve using order of Ops. • = 3714.62 cm3

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