Volume

Volume of Prisms Using formulas to find the volumes of rectangular and triangular prisms

Suppose your teacher had a bag of your favorite candy, but you are only allowed to take the amount of candy that will fit in one of the following bowls. Which bowl would you take and why?

Bowl A

Bowl B

Bowl C

Objective •

Given a rectangular or triangular prism, you will find its volume.

Purpose •

• •

Companies that export products overseas need to know how many items can fit inside a container. Knowing volume is a 6th and 7th grade standard. There is one item on the CAHSEE related to volume.

How many cubes are needed to fill this container?

How many cubes are needed to fill this container?

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How many cubes are needed to fill this container?

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How many cubes are needed to fill this container?

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How many cubes are needed to fill this container?

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How many cubes are needed to fill this container?

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How many cubes are needed to fill this container?

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How many cubes are needed to fill this container?

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How many cubes are needed to fill this container?

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How many cubes are needed to fill this container?

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How many cubes are needed to fill this container?

What is volume? •

Volume is the number of cubic units needed to fill a three-dimensional figure.

Which of the following is a description of volume?

1.

2.

3.

The amount of wrapping paper used to wrap a box. The amount of tile used on a floor. The number of dice needed to fill a box.

Volume of a rectangular prism

V  l  w  h or V  l wh where l is the length, w is the width, and h is the height. h

l

w

Volume of a Prism or Cylinder

V  B  h or V  Bh

where B is the area of the base and h is the height. h h

h B

B

B

Name that formula 1. 2.

3.

4.

Determine who will be partner A and partner B. Partner A will name one of the following: rectangular prism, triangular prism or cylinder. Partner B will describe the formula used to find the volume of the object Partner A names. After naming all three objects switch roles.

These are containers…

Container Cargo •

The Port of Long Beach is the 12th busiest container cargo port in the world.

In 2006, the Port of Long Beach handled: • • • •

•

More than 7.3 million containers (TEUs) Cargo valued at more than $100 billion More than 85 metric tons of cargo On average, the equivalent of 19,900 20-foot containers (TEUs) each day 5,300 vessel calls

The Port’s loaded containers account for: • • •

33 percent moving through all California ports 26 percent moving through all West Coast ports 13 percent moving through all U.S. ports

Find the volume of the rectangular prism Step 1: Use the formula for the volume of a rectangular prism

V  l wh

Step 2: Identify

l , w, and h

l  20 ft w  8 ft h  8.6 ft

8.6 ft

Step 3: Substitute 20 for 8 for w, and 8.6 for h.

20 ft 8 ft

l

,

V  (20)(8 (20) wh)(8. (20)(8) h 6) 3 Step 4: Simplify V  1,376 ft

Finding the volume of a rectangular prism 1.

2.

3.

Determine who will be partner A and partner B. Partner A will describe how to find the volume of prism A. Partner B will describe how to find the volume of prism B. 3yd

5yd

4cm 9yd

Prism A

12cm

2cm

Prism B

Find the volume of the rectangular prism Step 1: Use the formula for the volume of a rectangular prism

8.6 ft

40 ft

8 ft

V  l wh

Step 2: Identify l , w, and h

l  40 ft w  8 ft h  8.6 ft Step 3: Substitute 40 for 8 for w, and 8.6 for h.

l

,

V  (40)(8 (40) wh)(8. (40)(8) h 6) Step 4: Simplify Check my answer

Need a hint? Press the spacebar

V  2,752 ft

3

Find the volume of the rectangular prism

The volume of the rectangular prism is 2,752 ft3. Try again

Find the volume of the rectangular prism formed by four containers Step 1: Use the formula for the volume of a rectangular prism

V  l wh

17.2 ft

40 ft

16 ft

Step 2: Identify l , w, and h

l  40 ft w  16 ft h  17.2 ft Step 3: Substitute 40 for 16 for w, and 17.2 for h.

l

,

V  (40)(16 (40)(16) (40) wh)(1 h 7.2) Check my answer

Need a hint? Press the spacebar

Step 4: Simplify

V  11,008 ft

3

Find the volume of the rectangular prism formed by four containers

The volume of the rectangular prism is 11,008 ft3. Try again

Find the volume of the rectangular prism formed by nine containers Step 1: Use the formula for the volume of a rectangular prism

V  l wh

25.8 ft

40 ft

Step 2: Identify l , w, and h

l  40 ft w  24 ft h  25.8 ft

24 ft

Step 3: Substitute 40 for 24 for w, and 25.8 for h.

l

,

V  (40)(24) (40)(24 (40) wh )(2 h 5.8) Check my answer

Need a hint? Press the spacebar

Step 4: Simplify

V  24,768 ft

3

Find the volume of the rectangular prism formed by nine containers

The volume of the rectangular prism is 24,768 ft3. Try again

Find the volume of the triangular prism Step 1: Use the formula for the volume of a prism

V  Bh

Step 2: Identify B and h.

12 ft

12 ft 7 ft

10 ft

The area 1 Aofthe (1 (10 0)( )h7) base (5)( 7) 35 2 2 is 35 ft .

50 ft

B  35 ft 2 h  50 ft

Area of a triangle Remember B is the area Step 3: Substitute 35 for B, of the base. In this case, and 50 for h. the area of the triangle!!

1 A  bh 2 V  (35) (35)(50) h Step 4: Simplify

V  1,750 ft

3

Finding the volume of a triangular prism 1.

2.

3.

Determine who will be partner A and partner B. Partner A will describe how to find the volume of prism A. Partner B will describe how to find the volume of prism B.

Prism A

6cm

Prism B

10cm 8cm

18cm

13 ft

13 ft 9 ft

8 ft

36 ft

Find the volume of the triangular prism Step 1: Use the formula for the volume of a prism

V  Bh

Step 2: Identify B and h.

25m

B  14,030m 2 h  25m

The area of the base 2

is 14,030m . Need a hint? Check my answer Press the spacebar

Step 3: Substitute 14,030 for B, and 25 for h.

V  (14,030) (14,030)(2 h 5) Step 4: Simplify

V  350,750m

3

Find the volume of the triangular prism

Try again

The volume of the triangular prism is 3 350,750 m .

Find the volume of the triangular prism Step 1: Use the formula for the volume of a prism

V  Bh

7.5in 9in

18.5in

Step 2: Identify B and h.

B  83.25in 2 h  7.5in Remember B is the area of the base. In Step this case, 3: Substitute 83.25 for B, the area of the and triangle!! 7.5 for h.

V  (83.25) (83.25)(7. h 5)

The area

Step 4: Simplify

1

(18.5 (h9) (185)( .5))9) A  (9.2 of the base A 83.25 2 2 answer

Check my in is 83.25

.

Need a hint? Press the spacebar

V  624.375in

3

Find the volume of the triangular prism

Try again

The volume of the triangular prism is 624.375 in3.

This is a Petroleum Coke Shed at the Port of Long Beach Aerial view

This pet coke shed is a triangular prism

Petroleum Coke • •

AKA pet coke The Port of Long Beach is the largest pet coke exporting facility on the West Coast

Petroleum Coke • • • •

Dry bulk cargo A byproduct of oil refining Used in many countries as an industrial fuel source Used in the manufacture of dry cells and electrodes

Find the volume of the triangular prism Step 1: Use the formula for the volume of a prism

Aerial view

479.4 ft 100.6 ft

130.9 ft

The area 1 1 the base A(65.45)(100.6) (130.9 (130 .9)h0.6) AAof )(10 6,584.27

2 2 Need a hint? 2 Check my answer is 6584.27 ft . Press the spacebar

V  Bh

Step 2: Identify B and h.

B  6584.27 ft 2 h  479.4 ft Step 3: Substitute 6584.27 for B, Remember is thefor area andB479.4 h. of the base. In this case, the area of the triangle!! Step 4: Simplify

V  (6584.27 (6584.27))(47 h 9.4)

V  3,156, 499.038 ft

3

Find the volume of the triangular prism

Aerial view

Try again

The volume of the triangular prism is 3,156,499.038 ft3.

Find the volume of each prism 2. 4m

1.

5mm

13mm 12mm

18mm

6m

11m

V V  mm 540 264 m VVVV 384 in VV357.84 540 mm 264 myd

3 33

333 3 3  384inyd 357.84

4.

3. 5.6yd 21.3yd

3yd

5in

5in

8in

6in

16in

Let’s wrap it up!

Give a brief explanation of how to find the volume of the following prism:

19ft