## 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:

Answer:

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 = 48Â + 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:

Answer:

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?

Answer:

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?

Answer:

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?

Answer:

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 Bâ€™s base is \(\frac{2}{3}\) the area of Prism Aâ€™s base, what is the height of Prism B?

Answer:

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

=Â 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.

Answer:

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.Â 18 x 3 x 2 = 108 cubic centimetres

2.Â 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.Â 6 x 4Â 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:

Answer:

Volume = length x width x height

1.Â 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?

Answer:

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 cubeâ€™s edge?

Answer:

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?

Answer:

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?

Answer:

Given,

The total volume of three prisms = 518 cubic feet.

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

Now,Â 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