VOLUME of Rectangular Prisms 6 3 1 1

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=lxwxh V = B h (B = area base) 1. Copy the equation (don’t just solve in your head) 2. Substitute the numbers for the variables 3. Solve

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.

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.

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

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

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

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

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

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

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.

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

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

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

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

Level 2

FIND THE VOLUME OF THIS RECTANGULAR PRISM: 3 mm 2 mm 12 mm V=lxwxh V = 12 x 3 V = 72 mm 2

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

Finding the Volume of Rectangular Prisms The given measurements represent whole or partial kilometers. 8 km 3. 9 km 6. 2 km V=lxwxh V = 6. 2 x 3. 9 x 8 193. 44 ⅛ What W 1. S The Let’s 9 o, 8 hat What the given height length width divide write is volume theis is measurements the that it is product 93 as 1 -½ ¼ by remainder kilometers. fraction. is an of 8. kilometers. 1 -⅛ aimproper What kilometer. ofcubic theexpressed isrepresent numerators? denominators? the km. fraction. whole as whole number a fraction? or partial quotient? kilometers. cubic km

Level 3

2 in 4 in

2 in 4 in

Vblue = l x w x h Vblue = 2 x 2 2 in Vblue = 8 in 3 4 in 2 in 4 in

Vgreen = l x w x h Vgreen = 2 x 4 2 in Vgreen = 16 in 3 4 in 2 in 4 in

Vtotal = 8 + 16 2 in Vtotal = 24 in 3 4 in 2 in 4 in

Your Turn

Your Turn V=lxwxh V = 5 x 10 x 4 V = 200 cm 3

Your Turn V=lxwxh V = 3 x 10 x 7 V = 210 cm 3

Your Turn V = 200 + 210 V = 410 cm 3

Level 4

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=lxwxh 3750 = l x 25 x 3 3750 = l x 75 75 75 50 m

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=lxwxh 16 = 4 x 2 x h 16 = 8 x h 8 8 2 m

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.