## Engage NY Eureka Math 5th Grade Module 5 Lesson 6 Answer Key

### Eureka Math Grade 5 Module 5 Lesson 6 Problem Set Answer Key

Question 1.
Find the total volume of the figures, and record your solution strategy.
a. Volume: ______________
Solution Strategy:

Volume = length x width x height

V= 14 x 10 x 3

V = 420 cubic centimetres.

Solution strategy :
I added the height of 2 cubes to get 10 cm and applied volume formula

b. Volume: ______________
Solution Strategy:

1.

Volume = length x width x height

V = 7 x 4 x 3

V = 84 cubic inches

2.

Volume = 15 x 4 x 6

V = 360 cubic inches

Total volume = 84 + 360 = 444 cubic inches

Solution strategy = Calculated volume of each prism individually.

c. Volume: ______________
Solution Strategy:

1.

Volume = length x width x height

V = 4 x3 x 4

V = 48 cubic centimeters

2.

Volume = 10 x 3 x 2

V = 60 cubic centimeters

Total volume = 48  + 60

V = 108 cubic centimetres.

Solution strategy:

The width of the shape 1 is 10 – 6 = 4 cm ,

Then i calculate dthe volume individually and added them.

.

d. Volume: ______________
Solution Strategy:

Volume = length x width x height

1.

V = 8 x 3 x 6

V = 144 cubic centimeters

2.

Volume = 10 X 3 X 6

v = 180 cubic centimeters

Total volume = 144 + 180 = 324 Cubic centimeters

Solution strategy:

The height of the shape 1. is 12 – 6 = 6 cm

Then I caluculated the volume individually and added them together.

Question 2.
A sculpture (pictured below) is made of two sizes of rectangular prisms. One size measures 13 in by 8 in by 2 in. The other size measures 9 in by 8 in by 18 in. What is the total volume of the sculpture? Let, the small size prisms be A and large sized prisms be B

Given the measurents of prism A =

length = 13, width = 8 and height = 2 inches

Number of A prisms = 6

Now, volume = 13 in x 8 in x 2 in

V = 208 cubic inches

Total volume of 6 prisms(A) =

V = 206 x 6

V = 1248

Also given the measurements of prism B =

Length = 9 in, width = 8 in and height = 18 inches

Volume = 9 in x 8 in x 18 in

V = 1296

Number of prisms B = 2

Now,

Volume = 1296 x 2

V = 2592

Now, the total volume of the sculpture =

Volume of prisms A and volume of prisms B

= 1,248 + 2592

= 3840

Therefore, total volume of sculpture = 3840 cubic inches

Question 3.
The combined volume of two identical cubes is 128 cubic centimeters. What is the side length of each cube?

Given the combined volume of two identical cubes = 128 cubic centimetres

So, 128 / 2 = 64

64 can be written as 4 x 4x 4

Therefore, the each side is 4 cm long.

Question 4.
A rectangular tank with a base area of 24 cm2 is filled with water and oil to a depth of 9 cm. The oil and water separate into two layers when the oil rises to the top. If the thickness of the oil layer is 4 cm, what is the volume of the water? Given, the bae area of tank = 24 sq. cm

The depth of water and oil poured into the tank = 9 cm

Given, the thickness of oil poured = 4 cm

So, 9 – 4 = 5

Now, the volume of water =

V = 24 x 5

V = 120

Therefore, the volume of the water = 120 cubic cm.

Question 5.
Two rectangular prisms have a combined volume of 432 cubic feet. Prism A has half the volume of Prism B.
a. What is the volume of Prism A? Prism B?
b. If Prism A has a base area of 24 ft2, what is the height of Prism A?
c. If Prism B’s base is $$\frac{2}{3}$$ the area of Prism A’s base, what is the height of Prism B?

Given, the combined volume of three prisms = 432 cubic feet,

The prism A has half the volume of prism B

So, 432/3

= 144

So, the volume of prism A = 144 cubic feet and prism B = 288 cubic fet

b.

Given, if the base area of prism A = 24 sq. feet

Now, height of the prism =

Volume / area

144/24

= 6

Therefore, the height of prism A = 6 feet

c.

Given , if the prism B’s base = 2/3 of the prism A’s

Now, the height of prism B =

2/3 X 26

=  16 sq. feet

So, the height of prism B = volume/ area

= 288/16

= 18

Therefore, the height of prism B = 18 feet

### Eureka Math Grade 5 Module 5 Lesson 6 Exit Ticket Answer Key

The image below represents three planters that are filled with soil. Find the total volume of soil in the three planters. Planter A is 14 inches by 3 inches by 4 inches. Planter B is 9 inches by 3 inches by 3 inches. Volume of A

= length x width x height

v = 15 X 3 X 3

v = 135 cubic inches

Volume of B =

length x width x height

V = = 9 x 3 x 4

V = 108 cubic inches

Volume of C =

length x width xheight

V = 3 X 3 X 6

V = 54 cubic inches

Total volume = 135 + 108 + 54

V= 297

Therefore, the total volume of planters = 297 cubic inches.

### Eureka Math Grade 5 Module 5 Lesson 6 Homework Answer Key

Question 1.
Find the total volume of the figures, and record your solution strategy.
a. Volume: _________________
Solution Strategy:

Volume = length x width x height

1. V= 13 x 2 x 2

V= 52 cubic inches

2. V = 2 x 2 x 5 = 20 cubic inches

Total volume = 52 + 20 = 72 cubic inches.

Solution strategey = 4/2 = 2 , the heigth of the bottom box = 2 inches

b. Volume: _________________
Solution Strategy:

Volume = length x width x height

1.  18 x 3 x 2 = 108 cubic centimetres

2.  21 x 9 x 7 = 1326 cubic centimetres

Total volume = 1,431 cubic centimetres.

Solution strategy:

Calculated each shape volume individually.

c. Volume: _________________
Solution Strategy:

Volume = length x width x height

1.  6 x 4  x 3 = 72 cubic mm

2. 11 x 3 x 4 = 132 cubic mm.

3. 3 x 3 x 5 =45 cubic mm.

Total volume =72 + 132 + 45 = 249

Therefore, total volume = 249 cubic mm

Solution strategy :

8 – 5 = 3 So, the width of box is 3 mm

d. Volume: _________________
Solution Strategy:

Volume = length x width x height

1.  12 x 4 x 9 = 432 cubic metres

2. 10 x 2 x 2 = 40 cubic metres

Total volume = 432 + 40 = 472

Therefore, total volume = 472 cubic metres.

Solution strategy:

11 – 9 = 2 , So, the height of the bottom shape is 2 m

Question 2.
The figure below is made of two sizes of rectangular prisms. One type of prism measures 3 inches by 6 inches by 14 inches. The other type measures 15 inches by 5 inches by 10 inches. What is the total volume of this figure? 1.

Given, the measurement of shape 1 =

3 inches by 6 inches by 14 inches

Now, volume of box 1 =

V = length X width Xheight

v= 3 X 6 X 14

V =252 cubic inches

Now, there are 2 oxes of same shape so,

2 x 252 =504 cubic inches

2. The measurements of box 2 =

15 inches by 5 inches by 10 inches

Volum =- 15 x 5 x 10

V = 750 cubic inches

Now, total volume = 504 cubic in. + 750 cubic in.

V =1,254 cubic inches.

Question 3.
The combined volume of two identical cubes is 250 cubic centimeters. What is the measure of one cube’s edge?

Given, the combined volume of indentical cubes = 250 cubic centimetres.

250 / 2 = 125 cubic cm.

125 can be written as 5 x 5 x 5

Therefore, the measurement of one cube’s edge = 5 cm

Question 4.
A fish tank has a base area of 45 cm2 and is filled with water to a depth of 12 cm. If the height of the tank is 25 cm, how much more water will be needed to fill the tank to the brim? Volume = length x width x height

V= area x height

Given, height = 25 cm and area = 45 sq. cm.

V = 45 x 25

V = 1,125 cubic cm.

Given, depth = 12 cm

So, 45 x 12 = 540 cubic cm.

Now, 1125 – 540 = 585

Therefore, 585 millilitre of water is needed to fill the tank

Question 5.
Three rectangular prisms have a combined volume of 518 cubic feet. Prism A has one-third the volume of Prism B, and Prisms B and C have equal volume. What is the volume of each prism?

Given,

The total volume of three prisms = 518 cubic feet.

Also given Prism A has one-third the volume of prism B

Now,  518 / 7 = 74 cubic feet

74 x 3 = 222 cubic feet

Therefore, the volume of prism A =74 cubic feet

Volume of prism B and C = 222 cubic feet

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