## Engage NY Eureka Math 5th Grade Module 5 Mid Module Assessment Answer Key

### Eureka Math Grade 5 Module 5 Mid Module Assessment Task Answer Key

Question 1.

Tell the volume of each solid figure made of 1-inch cubes. Specify the correct unit of measure.

Answer:

a. 12 cubic inches

b. 8 cubic inches

Question 2.

Jack found the volume of the prism pictured to the right by multiplying 5 × 8 and then adding 40 + 40 + 40 = 120. He says the volume is 120 cubic inches.

a. Jill says he did it wrong. He should have multiplied the bottom first (3 × 5) and then multiplied by the height. Explain to Jill why Jack’s method works and is equivalent to her method.

Answer :

Firstly, Jack figured the area of one slide 8 x 5 .

Then he realized 2 more slices.so, he added 40 + 40 + 40 which is 120

This is equivalent answer that he would have gotten if he multiplied (3 x 5) x 8

b. Use Jack’s method to find the volume of this right rectangular prism.

Answer:

According to Jack’s method,

Volume = 3 x 2 = 6

Now, 6+6+6+6+6 = 30

Therefore, the volume of the right rectangular prism is 30 cubic feet.

Question 3.

If the figure below is made of cubes with 2 cm side lengths, what is its volume? Explain your thinking.

Answer:

Given, the measurement of cube = 2 cm

Now, length = 6 x 2 = 12

Width = 5 x 2 = 10 and

Height = 6 x 2 = 12

Volume = length x width x height

V = 12 x 12 x 10

V = 1440 cubic centimetres

Solution strategy :

Firstly I counted the number of cubes and multiplied by 2

Then I calculated volume by using the formula.

Question 4.

The volume of a rectangular prism is 840 in^{3}. If the area of the base is 60 in2, find its height. Draw and label a model to show your thinking.

Answer:

Given, the volume of rectangular prism = 840 in ^{3}

The base area = 60 in ^{2}

Now, its height = volume / base area

= 840/60

= 14

Therefore, height of the rectangular prism = 14 inches.

Question 5.

The following structure is composed of two right rectangular prisms that each measure 12 inches by 10 inches by 5 inches and one right rectangular prism that measures 10 inches by 8 inches by 36 inches. What is the total volume of the structure? Explain your thinking.

Answer:

Given,

The measurements of two right rectangular prism =

12 x 10 x 5 = 600 cubic inches

600 x 2 = 1,200 cubic inches

Also given, the measurements of right rectangular prism =

10 x 8 x 36 = 2,880 cubic inches

Now, total volume = 1,200 + 2,880

V = 4080 cubic inches.

Solution strategy :

I calculated the volume of prisms with given measurementsand added them.

Question 6.

a. Find the volume of the rectangular fish tank. Explain your thinking.

b. If the fish tank is completely filled with water and then 90 0 cubic centimeters are poured out, how high will the water be? Give your answer in centimeters, and show your work.

Answer:

a.

Volume = length x width x height

V = 45 x 20 x 10

V = 9000

Therefore, the volume of fish tank = 9000 cubic centimetres.

b.

Given that,

900 cubic metres of water is poured out

We know that, volume of the fish tank is 9000 cubic metres

So, 9000 – 900 = 8100

Now, 8100/450

= 18

Therefore, the water is 18 cm high.

Question 7.

Juliet wants to know if the chicken broth in this beaker will fit into this rectangular food storage container. Explain how you would figure it out without pouring the contents in. If it will fit, how much more broth could the storage container hold? If it will not fit, how much broth will be left over? (Remember: 1 cm^{3} = 1 mL.)

Answer:

The volume of the storage container =

Volume = length x width x height

V = 20 x 15 x 7

V = 2100 cubic centimetres or 2.1 litres

The volume of the broth in beaker as given is 2.4 litres

Now, 2.4 – 2.1 = 0.3 litres

Therefore, Juliet is left with 0.3 litres or 300 ml broth.