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.

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

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

Volume is the space that a figure occupies 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 This prism holds 3 layers of 9 cubic units for a total of 27 cubic units 1 cubic unit 1unit V = 27 cubic units

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

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

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

We know that the volume of a rectangle is …. 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 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

Base Area V = Bh B = lw V = (9)(3) B = (3)(3) V = 27 cubic units B = 9 square units V = Bh V = (9)(3) V = 27 cubic 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 = l x w x h V = 12 x 2 x 3 V = 72 mm2

The given measurements represent whole or partial centimeters. Finding the Volume of Rectangular Prisms The given measurements represent whole or partial centimeters. cubic cm 8 3 4 5 2 1 7 2 V = l x w x h 8 Here is a rectangular prism. The given measurements represent whole or partial centimeters. Let’s multiply the length by the width by the height to find the volume. What is the product of the numerators? 35 What is the product of the denominators? 4 Let’s divide 35 by 4. What is the whole number quotient? 8. And what is the remainder expressed as a fraction? ¾ So, the volume is 8-¾ cubic cm. 3 4 7 2 1 5 2 35 × × = 4 35 4 35

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

Level 3

4 in 2 in 2 in 4 in 2 in 2 in 4 in

4 in 2 in

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

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

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

Your Turn

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

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

Your Turn V = 200 + 210 V = 410 cm3

Level 4

The volume of a swimming pool is 3750 cubic meters 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

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

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.