Warm-Up Exercises ANSWER 252in. 2 ANSWER 360 m 2 Lesson 10.7, For use with pages 550-558 1. Find the surface area of a rectangular prism that is 12 inches.

Warm-Up Exercises

ANSWER 252in.2

ANSWER 360 m2

Lesson 10.7, For use with pages 550-558

1. Find the surface area of a rectangular prism that is12 inches by 3 inches by 6 inches.

2. Find the surface area of a rectangular prism that is10 meters by 4 meters by 10 meters.

Copy:6.G.2 Apply the formula V = l w h to find volumes of rectangular prisms.

Warm-Up Exercises

Notepads

EXAMPLE 1 Counting Cubes in a Stack

Apply the formula V = l w h to find volumes of rectangular prisms.

Warm-Up Exercises

Notepads


A manufacturer stacks cube-shaped notepads and wraps them in plastic as shown in Example 1. The manufacturer then puts them into a rectangular box for shipping. How many notepads will fit into each box?


Warm-Up Exercises

Notepads


A manufacturer stacks cube-shaped notepads and wraps them in plastic as shown in Example 1. The manufacturer then puts them into a rectangular box for shipping. How many notepads will fit into each box?

To find the total number of notepads that will fit in one box, multiply the number of notepads in one layer by the number of layers. The notepads are stacked in 2 layers. Each layer is a rectangle that is 4 notepads long and 3 notepads wide.


Warm-Up ExercisesEXAMPLE 1 Counting Cubes in a Stack

Notepads in one layer

Number of layers




Number of notepads

=Number of layers




Number of notepads

=

4 3

Number of layers

2




Number of notepads

=

4 3 = 24

Number of layers

2




Number of notepads

=

ANSWER

The manufacturer can fit 24 notepads in one box. Check You can count the number of notepads in the front layer, then multiply that number by the number of layers going front to back.

4 3 = 24

Number of layers

2


Warm-Up ExercisesKEY CONCEPT Finding the Volume of a Prism


Warm-Up ExercisesEXAMPLE 2

Find the volume of the rectangular prism.

Finding the Volume of a Prism




Write the volume formula.





l w hV = Write the volume formula.






Substitute for l, w, and h.





l w hV =

8( 6.2 )= (3.9)









Simplify.


8( 6.2 )= (3.9)




l w hV =

= 193.44



Simplify.


8( 6.2 )= (3.9)




l w hV =

= 193.44



Simplify.

ANSWER

The volume is 193.44 cubic inches.


8( 6.2 )= (3.9)


Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2



1. What If? In Example 1, suppose a box can hold one more horizontal layer of notepads. How many notepads would fit in a box?




SOLUTION




To find the total number of notepads that will fit in one box, multiply the number of notepads in one layer by the number of layers. The notepads are stacked in 3 layers. Each layer is a rectangle that is 4 notepads long and 3 notepads wide.

SOLUTION




Number of layers




Number of notepads

=Number of layers




Number of notepads

=

4 3

Number of layers

3




Number of notepads

=

4 3 = 36

Number of layers

3




Number of notepads

=

ANSWER

4 3 = 36

Number of layers

3




Number of notepads

=

ANSWER

The manufacturer can fit 36 notepads in one box..

4 3 = 36

Number of layers

3



Find the volume of the rectangular prism with the given dimensions.




2. 5 m by 2 m by 4 m




2. 5 m by 2 m by 4 m





2. 5 m by 2 m by 4 m

lwhV = Write the volume formula.




2. 5 m by 2 m by 4 m






2. 5 m by 2 m by 4 m

5( 2 )= ( 4 )lwhV = Write the volume formula.





2. 5 m by 2 m by 4 m

5( 2 )= ( 4 )lwhV = Write the volume formula.


Simplify.




2. 5 m by 2 m by 4 m

5( 2 )= ( 4 )

= 40



Simplify.




2. 5 m by 2 m by 4 m

5( 2 )= ( 4 )

= 40

ANSWER



Simplify.


Warm-Up ExercisesGUIDED PRACTICE


2. 5 m by 2 m by 4 m

5( 2 )= ( 4 )

= 40

ANSWER

The volume is 40 cubic meters.



Simplify.

for Examples 1 and 2








3. 12.5 ft. by 6 ft. by 6 ft.







3. 12.5 ft. by 6 ft. by 6 ft.






3. 12.5 ft. by 6 ft. by 6 ft.






3. 12.5 ft. by 6 ft. by 6 ft.







3. 12.5 ft. by 6 ft. by 6 ft.



lwhV =12.5( 6 ) = ( 6 )





3. 12.5 ft. by 6 ft. by 6 ft.



lwhV =12.5( 6 ) = ( 6 )



Simplify.



3. 12.5 ft. by 6 ft. by 6 ft.



lwhV =12.5( 6 ) = ( 6 )

= 450



Simplify.



3. 12.5 ft. by 6 ft. by 6 ft.



lwhV =12.5( 6 ) = ( 6 )

= 450

ANSWER



Simplify.



3. 12.5 ft. by 6 ft. by 6 ft.



lwhV =12.5( 6 ) = ( 6 )

= 450

ANSWER

The volume is 450 ft3.



Simplify.



3. 12.5 ft. by 6 ft. by 6 ft.



Aquariums

Using the Formula for Volume



Aquariums

A pool at an aquarium is a rectangular prism that is 30 meters wide and 12 meters deep.Its volume is 21,600 cubic meters. How long is the pool?




Aquariums


SOLUTION




Aquariums


SOLUTION





Aquariums


SOLUTION

V = lwh Write the volume formula.




Aquariums


SOLUTION


Substitute for V, w, and h.




Aquariums


SOLUTION

V = lwh

21,600 = l 30 12






Aquariums


SOLUTION

V = lwh

21,600 = l 30 12



Simplify.




Aquariums


SOLUTION

V = lwh

21,600 = l 30 12

21,600 = l 360



Simplify.




Aquariums


SOLUTION

V = lwh

21,600 = l 30 12

21,600 = l 360



Write a related division equation

Simplify.




Aquariums


SOLUTION

V = lwh

21,600 = l 30 12

21,600 = l 360

l = 21,600 360




Simplify.




Aquariums


SOLUTION

Simplify.




Simplify.


V = lwh

21,600 = l 30 12

21,600 = l 360

l = 21,600 360



Aquariums


SOLUTION

Simplify.




Simplify.


V = lwh

21,600 = l 30 12

21,600 = l 360

l = 21,600 360

l = 60


Warm-Up Exercises

ANSWER

The length of the pool is 60 meters.

EXAMPLE 3 Using the Formula for Volume


Warm-Up ExercisesGUIDED PRACTICE for Example 3



In Exercises 4 and 5, the solids are rectangular prisms.




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?





SOLUTION





SOLUTION






SOLUTION






SOLUTION







SOLUTION

V = lwh

3,750 = l 25 3







SOLUTION

V = lwh

3,750 = l 25 3



Simplify.





SOLUTION

V = lwh

3,750 = l 25 3

3,750 = l 75



Simplify.





SOLUTION

V = lwh

3,750 = l 25 3

3,750 = l 75




Simplify.





SOLUTION

V = lwh

3,750 = l 25 3

3,750 = l 75

l = 3,750 75




Simplify.





SOLUTION

V = lwh

3,750 = l 25 3

3,750 = l 75

l = 3,750 75

Simplify.




Simplify.





SOLUTION

V = lwh

3,750 = l 25 3

3,750 = l 75

l = 3,750 75

l =50Simplify.




Simplify.


Warm-Up Exercises

ANSWER

The length of the pool is 50 meters.

GUIDED PRACTICE for Example 3



5. The volume of a bathtub is 16 cubic feet. The bathtub is 4 feet long and 2 feet wide. How deep is the bathtub?




SOLUTION




SOLUTIONWrite the volume formula.




SOLUTION





SOLUTION






SOLUTION

V = lwh

16 = 4 2 h








Simplify.


V = lwh

16 = 4 2 h





Simplify.


V = lwh

16 = 4 2 h

16 = 8 h






Simplify.


V = lwh

16 = 4 2 h

16 = 8 h






Simplify.


V = lwh

16 = 4 2 h

16 = 8 h

h = 16 8



SOLUTION

Simplify.




Simplify.


V = lwh

16 = 4 2 h

16 = 8 h

h = 16 8



SOLUTION

Simplify.




Simplify.


ANSWER

The depth of the bathtub is 2 feet.

V = lwh

16 = 4 2 h

16 = 8 h

h = 16 8

h = 2

Warm-Up ExercisesSKILL PRACTICE for Lesson 10.7


8,000 cm³ 6,851 in.³ 330 in³

0.45 km³ 323.4375 mm³ 124.3125 yd³

To get the volume, you multiply the length, width, and height, not add them.

The correct answer is 420 ft³

Warm-Up ExercisesSKILL PRACTICE for Lesson 10.7


h = 2.5 ft w = 2 cm l = 20 m

Warm-Up ExercisesEXIT PASS

1. 2.

For use after Lesson 10.7Find the volume of the prism.

31,320cm3ANSWER6750 m3ANSWERFind the volume of a rectangular prism that is feet by feet by feet.

3.7 8 3 168 ft3ANSWER


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Warm-Up ExercisesANIMATED MATH for Lesson 10.7


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Warm-Up ExercisesLESSON QUIZ for Lesson 10.7


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Warm-Up Exercises ANSWER 252in. 2 ANSWER 360 m 2 Lesson 10.7, For use with pages 550-558 1. Find the surface area of a rectangular prism that is 12 inches.

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