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Geometry

Geometry. Content Standard: MG. 1.3 Know and use the formulas for the volume of triangular prisms and cylinders; compare these formulas and explain the similarity between them and the formula for the volume of a rectangle solid. Volume of Rectangular and Triangular Prisms.

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Geometry

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  1. Geometry Content Standard: MG. 1.3 Know and use the formulas for the volume of triangular prisms and cylinders; compare these formulas and explain the similarity between them and the formula for the volume of a rectangle solid. Volume of Rectangular and Triangular Prisms Student Objective: Students will use the formula for volume of triangular prisms and use it to compare and explain the similarities with the formula for volume of a rectangular solid, following steps, creating three-dimensional manipulatives, using a ruler to find the units of measurements, and scoring an 80% proficiency on an exit slip.

  2. Volume • Volume – the amount of space occupied by an object. Example: The VOLUME of this cube is all the space contained by the sides of the cube, measured in cube units (units3). h w l

  3. Volume • Volume – To calculate the volume of a prism, we first need to calculate the area of the BASE of the prism. Example: The AREA of the base of this rectangular prism is l x w. h w l

  4. Volume • Volume – Once we know the area of the base, this is then multiplied by the height to determine the VOLUME of the prism. We find that: Volume = Area of Base x Height Volume = (l x w) x h h w l

  5. Volume • Volume (rectangular prism) Formula: V = B x h V = l x w x h h w l

  6. Volume • Find the volume of this prism… Formula: V = B x h V = l x w x h 7 cm 4 cm 5 cm

  7. Volume • Find the volume of this prism… Formula: V = B x h V = l x w x h V = 5cm x 4cm x 7cm 7 cm 4 cm 5 cm

  8. Volume • Find the volume of this prism… Formula: V = B x h V = l x w x h V = 5cm x 4cm x 7cm V = 140cm3 7 cm 4 cm 5 cm

  9. Volume • Does it matter which side is the base? Formula: V = B x h V = l x w x h V = 7cm x 4cm x 5cm 5 cm 4 cm 7 cm

  10. Volume • Volume of a Triangular Prism

  11. Volume • The same principles apply to the triangular prism. To find the volume of the triangular prism, we must first find the area of the triangular base (shaded in yellow). h b

  12. Volume • To find the area of the Base… Area (triangle) = b x h 2 This gives us the Area of the Base (B). h b

  13. Volume • Now to find the volume… We must then multiply the area of the base (B) by the height (h) of the prism. This will give us the Volume of the Prism. B h

  14. Volume • Volume of a Triangular Prism Volume (triangular prism) V = B x h B h

  15. Volume Volume V = B x h • Together…

  16. Volume Volume V = B x h V = (8 x 4) x 12 2 • Together…

  17. Volume Volume V = B x h V = (8 x 4) x 12 2 V = 16 x 12 • Together…

  18. Volume Volume V = B x h V = (8 x 4) x 12 2 V = 16 x 12 V = 192 cm3 • Together…

  19. Volume Find the Volume • Your turn…

  20. Volume • In your notebook: draw the two prisms. • Measure with a ruler and find the dimensions for each prism and record them in your notebook. • Find the Volume of both, the rectangular prism and the triangular prisms. • Your turn…

  21. Reflection: How does the volume of a rectangular Prism compare to the volume of a triangular Prism? Definition in your own words Definition: the amount of space occupied by an object. Volume Non-Examples: Examples:

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