GEOMETRY-CYLINDER-powerpoint presentation

report on cylinder

1. Dr. Allan Q. Quismundo Professor GEOMETRY Prepared by: Marjorie M. Estuita MMA 104

2. SURFACE AREA & VOLUME CYLINDER OF A TOPIC….

3. DID YOU KNOW?

4. To find the surface area of a cylinder , open the cylinder and flatten it out. When you unfold a cylinder, the lateral area is shaped like a rectangle . The bases are shaped like circles . To get the total surface area of a cylinder, add the area of the two circle bases and the lateral area of the rectangle. The length of the rectangle is the same as the circumference of the circle as it wraps completely around the circle.

5. Surface Area = Area of two circles + Area of the rectangle = 2 × Area of base + Lateral Area = 2 × πr² + 2πr × h = 2πr² + 2πrh Let the length of the rectangle = 2πr width = height (h)

6. SA = 2 π r² + 2 π rh Example 1: Find the surface area of the cylinder given the figure. = 2 π(8)² + 2π(8)(15) = 128π + 240π = 368π ≈ 1,155.52 cm²

7. SA = 2 π r² + 2 π rh Example 2: Find the surface area of the cylinder given the figure. = 2 π( 5 )² + 2π( 5 )( 8 ) = 50 π + 80 π = 130 π ≈ 408.2 cm²

8. The volume of a cylinder is  the density of the cylinder which signifies the amount of material it can carry or how much amount of any material can be immersed in it .  DID YOU KNOW?

9. V = Area of the Circle (Base) x height Example 1: Find the volume of the cylinder given the figure. V = π r ² h = π (8)²(15) = 960 π ≈ 3,014 . 4 cm³

10. V = Area of the Circle (Base) x height Example 2: Find the volume of the cylinder given the figure. V = π r ² h = π (5)²(8) = 200 π ≈ 628 cm³

11. An OBLIQUE CYLINDER does not have right angles between the sides and the base. OBLIQUE CYLINDER OBLIQUE means slanted, not parallel or perpendicular

12. Cavalieri’s Principle Bonaventura Francesco Cavalieri (1598–1647; an Italian mathematician) Cavalieri's principle tells us that if the cross sections of the figure have equal areas at all spaces and the altitude of both the solids are the same, then the volumes are equal. Therefore, the volume of an oblique cylinder is the same as the volume of a right cylinder. V = πr2h OBLIQUE CYLINDER

13. V = Area of the Circle (Base) x height Example 1: Find the volume of the cylinder given the figure. V = π r ² h = π (5)²(17) = 425 π ≈ 1,334.5 cm³

14. Thank you for listening and have a nice day…