## Engage NY Eureka Math 5th Grade Module 5 Lesson 4 Answer Key

### Eureka Math Grade 5 Module 5 Lesson 4 Problem Set Answer Key

Question 1.

Each rectangular prism is built from centimeter cubes. State the dimensions, and find the volume.

a.

Length: _______ cm

Width: _______ cm

Height: _______ cm

Volume: _______ cm ^{3}

Answer:

Length: 5 cm

Width: 2 cm

Height:2 cm

Volume:

Volume = length x width x height

5 x 2 x 2 = 20

= 20 cm ^{3}

b.

Length: _______ cm

Width: _______ cm

Height: _______ cm

Volume: _______ cm^{3}

Answer;

Length: 3 cm

Width: 2 cm

Height: 4 cm

Volume:

Volume = length x width x height

3 x 2 x 4 = 24

= 24 cm ^{3}

c.

Length: _______ cm

Width: _______ cm

Height: _______ cm

Volume: _______ cm^{3}

Answer:

Length: 4 cm

Width: 2 cm

Height: 4 cm

Volume:

Volume = length x width x height

4 x 2 x 4 = 32

= 32 cm ^{3}

d.

Length: _______ cm

Width: _______ cm

Height: _______ cm

Volume: _______ cm^{3}

Answer:

Length: 4 cm

Width: 3 cm

Height:3 cm

Volume:

Volume = length x width x height

4 x 3 x 3 = 36

= 36 cm ^{3}

Question 2.

Write a multiplication sentence that you could use to calculate the volume for each rectangular prism in Problem 1. Include the units in your sentences.

a. _____________

b. _____________

c. ______________

d. ______________

Answer:

Multiplication sentences:

a. 5 cm x 2 cm x 2 cm = 20 cm ^{3}

b. 3 cm x 2 cm x 4 cm = 24 cm ^{3}

c. 4 cm x 2 cm x 4 cm = 32 cm ^{3}

d. 4 cm x 3 cm x 3 cm = 36 cm ^{3}

Question 3.

Calculate the volume of each rectangular prism. Include the units in your number sentences.

a.

V= ________________

Answer:

Volume = length x width x height

Given, length = 4 inches

Width = 3 inchesÂ and

height = 4 inches

V= 4 in x 3 in x 4 in

V=Â 48 in ^{3}

Therefore, Volume = 4 in x 3 in x 4 in = 48 in ^{3}

b.

V = ______________

Answer:

Volume = length x width x height

Given, length = 3 metres

Width = 2 metresÂ and

height = 6 metres

V= 3 m x 2 m x 6 m

V=Â 36 m ^{3}

Therefore, Volume = 3 m x 2 m x 6 m =Â 36 mÂ ^{3}

Question 4.

Tyron is constructing a box in the shape of a rectangular prism to store his baseball cards. It has a length of 10 centimeters, a width of 7 centimeters, and a height of 8 centimeters. What is the volume of the box?

Answer:

Given,

The measurements of box are,

Length = 10 centimetres

Width = 7 centimetres

Height = 8 centimetres

Volume = length x width x height

V = 10 x 7 x 8

V = 560 cm ^{3}

Therefore, the volume of the box isÂ 560 cubic centimetres.

Question 5.

Aaron says more information is needed to find the volume of the prisms. Explain why Aaron is mistaken, and calculate the volume of the prisms.

Answer:

a.

Aaron can multiply area x width to find the volume

We know that,

Area = length x width

Volume = length x width x height

Given, Area = 60 sq. cm

And width = 5 cm

Now, V = 60 x 5 = 300 cm ^{3}

b.

Aaron can multiply area x height to find the volume

Given,

Area = 20 sq. inches and

Height = 12 inches

Now, volume = 20 sq. inches x 12 inches

V= 20 x 12 = 240 in ^{3}

### Eureka Math Grade 5 Module 5 Lesson 4 Exit Ticket Answer Key

Question 1.

Calculate the volume of prism.

Length: _______ mm

Width: _______ mm

Height: _______ mm

Volume: ____________ mm^{3}

Write the multiplication sentence that shows how you calculated the volume. Be sure to include the units.

Answer:

Length: 2 mm

Width: 2 mm

Height: 4 mm

Volume: 16 mm ^{3}

Multiplication sentence :

Volume = length x width x height

V= 2 x 2 x 4 =16 mm ^{3}

Question 2.

A rectangular prism has a top face with an area of 20 ft2 and a height of 5 ft. What is the volume of this rectangular prism?

Answer:

Volume = length x width x height

Given,

Area of rectangular prism = 20 sq. ft. and

Height = 5 feet

Volume = 20 x 5 = 100 ft ^{3}

Therefore, the volume of the rectangular prism = 100 ft ^{3}

### Eureka Math Grade 5 Module 5 Lesson 4 Homework Answer Key

Question 1.

Each rectangular prism is built from centimeter cubes. State the dimensions, and find the volume.

a.

Length: _______ cm

Width: _______ cm

Height: _______ cm

Volume: _______ cm^{3}

Answer :

Length: 5 cm

Width: 2 cm

Height: 4 cm

Volume: 40 cm^{3}

b.

Length: _______ cm

Width: _______ cm

Height: _______ cm

Volume: _______ cm ^{3}

Answer:

Length: 3 cm

Width: 2 cm

Height: 5 cm

Volume: 30 cm ^{3}

c.

Length: _______ cm

Width: _______ cm

Height: _______ cm

Volume: _______ cm^{3}

Answer :

Length: 4 cm

Width: 2 cm

Height: 4 cm

Volume: 32 cm ^{3}

d.

Length: _______ cm

Width: _______ cm

Height: _______ cm

Volume: _______ cm ^{3}

Answer:

Length: 8 cm

Width: 3 cm

Height: 3 cm

Volume: 72 cm ^{3}

Question 2.

Write a multiplication sentence that you could use to calculate the volume for each rectangular prism in Problem 1. Include the units in your sentences.

a. ______________

b. ______________

c. ________________

d. ________________

Answer:

a. 5 cm x 2 cm x 4 cm = 40 cm ^{3}

b. 3 cm x 2 cm x 5 cm = 30 cm ^{3}

c. 4 cm x 2 cm x 4 cm = 32 cm ^{3}

d. 8 cm x 3 cm x 3 cm = 72 cm ^{3}

Question 3.

Calculate the volume of each rectangular prism. Include the units in your number sentences.

Answer:

a.

Given,

length = 8 inches

width = 4 inches and

Height = 8 inches

Volume = Length x width x height

V = 8 in x 3 in x 8 in = 256 in ^{3}

Therefore, Volume of rectangular prism = 256 in ^{3}

b.

Given,

length = 10 m

Width = 3 metres and

Height = 7 metres

Volume = length x width x height

V= 10 m x 3 m x 7 m

V= 210 m ^{3}

Therefore, the volume = 210 m ^{3}

Question 4.

Mrs. Johnson is constructing a box in the shape of a rectangular prism to store clothes for the summer. It has a length of 28 inches, a width of 24 inches, and a height of 30 inches. What is the volume of the box?

Answer:

Given, the measurements of the rectangular prism are

Length = 28 inches

Width = 24 inches and

height = 30 inches

Volume = length x width x height

V= 28 x 24 x 30 = 20,160 in ^{3}

Therefore, the volume of the prism = 20,160 in ^{3}

Question 5.

Calculate the volume of each rectangular prism using the information that is provided.

a. Face area: 56 square meters

Height: 4 meters

b. Face area: 169 square inches

Height: 14 inches

Answer:

a.

Area = 56 sq. cm

and height = 4 metres

Volume = area x height

V = 56 x 4 = 224 m ^{3}

Therefore, the volume of prism = 224 cm ^{3}

b.

Given,

Area = 169 sq. inches and

Height = 14 inches

Volume = Area x height

V = 169 x 14 = 2,366 in ^{3}

Therefore, the volume of the prism = 2,366 in ^{3}