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VOLUME of Rectangular Prisms

VOLUME of Rectangular Prisms. 6.3.1.1 Calculate the surface area and volume of prisms and use appropriate units, such as cm 2 and cm 3 . Justify the formulas used. Justification my involve decomposition, nets, or other models. 10.7 Notes. Volume of a Prism. V = l x w x h

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VOLUME of Rectangular Prisms

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  1. VOLUME of Rectangular Prisms 6.3.1.1 Calculate the surface area and volume of prisms and use appropriate units, such as cm2 and cm3. Justify the formulas used. Justification my involve decomposition, nets, or other models.

  2. 10.7 Notes Volume of a Prism • V = l x w x h • V = B h (B = area base) Copy the equation (don’t just solve in your head) Substitute the numbers for the variables Solve

  3. I can… • Calculate the volume of a rectangular prisms • Calculate the volume of irregular rectangular prisms Self Assessment 5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

  4. What is Volume? • Volume is the measure of the capacity of a container. • It is the measure of how much a container of a particular shape will hold - liquids, dry substances, etc.

  5. Cubic Units • Volume is measured in cubic units. • Use cubes to fill a rectangular prism such as a box.

  6. 1 unit(length) 1 unit(height) 1 unit(width) One Cubic Unit A unit might be measured in inches, feet, centimeters, etc.

  7. 1unit 1unit 1unit Volume is the space that a figure occupies. It is measured in cubic units. We can begin by stacking the cubic units in the bottom of the prism 3units This prism holds 9 cubic units in the bottom layer. The volume of the given cube can be found by determining how many cubic units will fit inside the cube. 3units We can continue to stack these layers until the prism is full. 3units 1 cubic unit This prism holds 3 layers of 9 cubic units for a total of 27 cubic units V = 27 cubic units

  8. How many cubic units is this rectangle? What did you find? Yes, it is 8 cubic units!

  9. How about this one? Remember… there are some cubes you can’t see! Watch...

  10. Now Count Them What did you find? Yes! There are 12 cubic units!

  11. What’s the formula? We know that the volume of a rectangle is …. L x W x H = Volume This means we take the length times the width, then multiply that by the height.

  12. Let’s try it! L = 3 H = 3 W = 2 3 x 3 x 2 = 18 cubic units

  13. What’s another formula? B x h= Volume B = the area of the base h = height (# of layers) This means we find the area (how many cubes) of one layer

  14. 3units 3units 3units h w l Base Area B = lw B = (3)(3) B = 9 square units V = Bh V = (9)(3) V = 27 cubic units

  15. Find the volume of this one! A =Bh A =12 x 2 24 cubic units

  16. Level 2

  17. FIND THE VOLUME OF THIS RECTANGULAR PRISM: 3 mm 2 mm 12 mm V = l x w x h V = 12 x 2 x 3 V = 72 mm2

  18. Finding the Volume of Rectangular Prisms The given measurements represent whole or partial centimeters. 8 cubic cm 1 V = l x w x h 8 35 5 7 1 7 5 3 3 × × = 4 35 4 2 2 4 4 2 1 2 35

  19. Finding the Volume of Rectangular Prisms The given measurements represent whole or partial kilometers. 193.44 cubic km 3.9 km V = l x w x h 6.2 km 8 km V = 6.2 x 3.9 x 8 ⅛ The given measurements represent whole or partial kilometers. Let’s write it as an improper fraction. The width is 3 kilometers. Let’s write it as an improper fraction. The length is 1-½ kilometers. Let’s write that fraction. Let’s divide 9 by 8. What is the whole number quotient? So, the volume is 1-⅛ cubic km. 8 What is the product of the numerators? 9 What is the product of the denominators? The height is ¼ of a kilometer. 1. What is the remainder expressed as a fraction?

  20. Level 3

  21. 2 in 2 in 4 in 4 in 2 in 2 in 4 in 2 in 2 in 4 in

  22. 2 in 4 in 2 in 2 in 4 in

  23. 2 in Vblue = l x w x h Vblue = 2 x 2 x 2 4 in Vblue = 8 in3 2 in 2 in 4 in

  24. 2 in Vgreen = l x w x h Vgreen = 2 x 2 x 4 4 in Vgreen = 16 in3 2 in 2 in 4 in

  25. 2 in Vtotal = 8 + 16 Vtotal = 24 in3 4 in 2 in 2 in 4 in

  26. Your Turn

  27. Your Turn V = l x w x h V = 5 x 10 x 4 V = 200 cm3

  28. Your Turn V = l x w x h V = 3 x 10 x 7 V = 210 cm3

  29. Your Turn V = 200 + 210 V = 410 cm3

  30. Level 4

  31. The volume of a swimming pool is 3750 cubic meters. The pool is 25 meters wide and 3 meters deep. How long is the pool? V = l x w x h 3750 = l x 25 x 3 3750 = l x 75 50 m 75 75

  32. The volume of a bathtub is 16 cubic feet The bathtub is 4 feet long and 2 feet wide. How deep is the bathtub? V = l x w x h 16 = 4 x 2 x h 16 = 8 x h 2 m 8 8

  33. I can… • Calculate the volume of a rectangular prisms • Calculate the volume of irregular rectangular prisms Self Assessment 5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

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