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02.26.2019

Learn how to calculate the volume of various shapes such as cubes, spheres, cylinders, pyramids, and prisms. Explore the concepts of surface area and apply the appropriate formulas. Resources, examples, and step-by-step calculations provided.

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02.26.2019

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  1. 02.26.2019 Bell Ringer Agenda • Bell Ringer • Volume Video: https://www.youtube.com/watch?v=aPXvrFMyhSU • Cornell notes • Topic: Volume • E.Q. How can I calculate the volume of a given shape? • KWL Chart

  2. Volume & Surface Area Section 6.2

  3. Volume • The volume is a measure of the space inside a solid object. • Volume is measure of 3 dimensions. • The units of volume are cube length or length3. • Example of volume units are cm3, cubic feet, cubic meters or inches3.

  4. Surface Area • Surface area is the flat area on the surface of a three-dimensional object. • What you do is compute the area of all the sides of an object and then add them up.

  5. The Cube • For an arbitrary cube with edges that have length L, H, and W. The volume is V = LWH. • The surface area of the cube is the sum of the areas of each face. SA = 2LW + 2HW + 2LH. H W L

  6. Height Width Length How would you work out the volume?

  7. The Sphere • The volume of a sphere with radius r, is V = (4/3)πr3. • The surface area is SA = 4πr2.

  8. The cylinder • The volume of the cylinder is height of the cylinder times the area of a circle. V = πr2h. • The surface area of a cylinder has two parts. The ends are circles so each circle has an area of πr2. The lateral surface can be thought of as a rectangle wound into a circle. One side of the rectangle is h, the other side is the circumference of the circle which is 2πr. 2πr h h

  9. Volume of a Cylinder r h A cylinder is a special type of prism with a circular cross-section. Volume = area of circular base × height

  10. The pyramid and cone • The pyramid and cone have similar formulas for their volume. The basic volume formula is V = (1/3)Ah. Where A is the area of the base. • For a pyramid, the area of the base A is just the area of a rectangle. • For a cone, the area of the base is the area of a circle. pyramid cone

  11. A prism is a 3-D shape that has a constant cross-section along its length. For example, this hexagonal prism has the same hexagonal cross-section throughout its length. Prisms This is called a hexagonal prism because its cross-section is a hexagon.

  12. Volume of a prism l h A A The volume of a prism is found by multiplying the area of its cross-section by its length or height.

  13. Volume of a prism What is the volume of this triangular prism? 7.2 cm 4 cm 5 cm Area of cross-section = ½ × 5 × 4 = 10 cm2 Volume of prism = 10 × 7.2 = 72 cm3

  14. Reference • https://www.asu.edu/courses/mat142ej/.../volume_and_surface_area_dalesandro.ppt

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