Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms

We included HMH Into Math Grade 6 Answer Key PDF Module 13 Lesson 2 Find Volume of Rectangular Prisms to make students experts in learning maths.

HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms

I Can find the volume of a rectangular prism using the formula V = lwh or V = Bh.

Spark Your Learning

The truck shown is delivering sand for a sand sculpture competition. How many trips must the truck make to deliver 15 cubic yards of sand? Explain your reasoning.
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 1
Answer:
12 trips

Explanation:
Given
l = 12 ft, w = 5 ft and h = 3 ft
Volume = 12 × 5 × 3 = 180 ft
Deliver 15 cubic yards of sand
\(\frac{180}{15}\) = 12 trips.

Turn and Talk Is there another formula that you could have used to find the volume of the bed of the truck? Explain.
Answer:
v = B × h

Explanation:
We can use the formula v = b × h to calculate the volume of the bed of the truck.

Build Understanding

Question 1.
A cube with edge length 1 unit and volume 1 cubic unit is filled with smaller cubes as shown. Find the volume of one small cube.
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 2
A. How many small cubes are there? Explain how you know.
Answer:
27

B. How does the combined volume of the small cubes compare to the volume of the large cube?
Answer:
A large cube consists of smaller cubes. The more the small cubes, the greater the large cube.

C. Complete the model.
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 3
What is the volume of one small cube? HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 4 cubic unit(s)
Answer:

D. Complete the model.
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 5
What b the edge length of one small cube? HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 4 unit(s)
Answer:

E. The formula for volume of a rectangular prism is V = lwh, where l and w are the length and width of the base and h is the height Find the
volume of one small cube using this formula.
V = __________ = _________ cubic unit(s)
Answer:

F. A cube with edge length \(\frac{2}{3}\) unit is shown. The cube b filled with the same smaller cubes as used In Parts A-E. Find the volume of the cube shown.
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 6
V = __________ = ___________ cubic unit(s)
Answer:
Given,
l = \(\frac{2}{3}\) , w = \(\frac{2}{3}\)  h = \(\frac{2}{3}\)
V = l × w × h
V = \(\frac{2}{3}\) × \(\frac{2}{3}\) × \(\frac{2}{3}\)
V = \(\frac{8}{27}\) cubic units.

Turn and Talk What is true about the edge lengths of a cube? How can you use this information to write a formula that uses exponent to find the volume of a cube?
Answer:

Step It Out

You can find the volume of a rectangular prism using the following formulas: V = Lwh or V = Bh (where B represents the area of the prism’s base, B = Lw).

Question 2.
Josh would like to know how much flour his container can hold.
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 7
A. The length is ___________ in. The width is ___________ in. The height is ___________ in.
Answer:
width = 8 in.
length = 8\(\frac{1}{2}\) = \(\frac{17}{2}\)
height = 12\(\frac{1}{2}\) = \(\frac{25}{2}\)

B. Substitute for the given variables and find the volume of the flour container.
V = Lwh
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 8
Answer:
HMH-Into-Math-Grade-6-Module-13-Lesson-2-Answer-Key-Find-Volume-of-Rectangular-Prisms-8

C. Josh’s container can hold HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 4 in3 of flour.
Answer:
Josh’s container holds 850 in3 of flour.

Turn and Talk Use the formula V = Bh to find the area of the flour container. What do you notice? Will this always be true? Explain why you think so.
Answer:

Check Understanding

Question 1.
What is the volume of the rectangular prism? Show your work.
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 9
Answer:
The volume of the rectangular prism is 10.56 in3.

Explanation:
Given,
l = 3\(\frac{1}{4}\) = \(\frac{13}{4}\) in.
w = 3\(\frac{1}{4}\) = \(\frac{13}{4}\) in.
h = 1 in.
volume of the rectangular prism = l × w × h
volume = \(\frac{13}{4}\) × \(\frac{13}{4}\) × 1
volume = \(\frac{169}{16}\)
volume of the rectangular prism is 10.56 in3.

Question 2.
What is the volume of a rectangular prism that has a base area of \(\frac{1}{8}\) in2 and a height of \(\frac{3}{4}\) in.?
Answer:
Given,
B = Area = \(\frac{1}{8}\) in2
height = \(\frac{3}{4}\)
Volume of the rectangular prsim = l × w × h
Volume = B × h
= \(\frac{1}{8}\) × \(\frac{3}{4}\)
= \(\frac{3}{32}\)
= 0.093 cubic inches.

On Your Own

Question 3.
Trent is putting in a sidewalk that is \(\frac{1}{18}\) yard thick, 9 yards long, and 1 yard wide. How many cubic yards of cement does he need?
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 10
Answer:
Cubic yards of cement = \(\frac{1}{2}\).

Explanation:
Given,
l = \(\frac{1}{18}\)
w = 9 yards
h = 1 yards
Volume of the cement = l × w × h
= \(\frac{1}{18}\) × 9 × 1
= \(\frac{1}{2}\) cubic yards.

Question 4.
Reason Explain how to find the volume of the cinder block wall with the window removed.
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 11
Answer:
Volume = (l × w × h) – w3

For Problems 5-8, find the volume of each figure.

Question 5.
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 12
Answer:
The volume of the cube = 343 cm3

Explanation:
Given,
a = 7 cm
Volume of the cube = a3
= 7 × 7 × 7
= 343 cm3

Question 6.
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 13
Answer:
The volume of the figure is 126299.25 in3

Explanation:
Given,
l = 72 in
w = 89\(\frac{1}{10}\) = \(\frac{891}{10}\)
h =20\(\frac{1}{4}\) = \(\frac{81}{4}\)
volume = l × w × h
= 70 × \(\frac{891}{10}\) × \(\frac{81}{4}\)
= 70 × \(\frac{(891 × 81)}{(10 × 4)}\)
= 126299.25 in3

Question 7.
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 14
Answer:
The volume of the figure is 1710 ft3

Explanation:
Given,
l = 15 ft
w = 18 ft
h = 6\(\frac{1}{3}\) = \(\frac{19}{3}\)
volume of the figure is l × w × h
= 15 × 18 × \(\frac{19}{3}\)
= 5 × 18 × 19
= 1710 ft3

Question 8.
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 15
Answer:
The volume of the figure is 33.64 ft3

Explanation:
Given,
l = 6\(\frac{1}{3}\) = \(\frac{19}{3}\)
w = 4\(\frac{1}{4}\) = \(\frac{17}{4}\)
h = 1\(\frac{1}{4}\) = \(\frac{5}{4}\)
Volume of the figure is l × w × h
= \(\frac{19}{3}\) × \(\frac{17}{4}\) × \(\frac{5}{4}\)
= \(\frac{(19 × 17 × 5 }{(3 × 4 × 4}\)
= \(\frac{1615}{48}\)
= 33.64 ft3

I’m in a Learning Mindset!

How did I use my prior knowledge of multiplying mixed numbers to find the volume of a rectangular prism?
Answer:
The volume of a rectangular prism multiplies the area of the base by its height.

Lesson 13.2 More Practice/Homework

Question 1.
Open-Ended Keesha is building a raised flower bed around a tree. Explain how to find the volume of soil she needs in order to fill the flower bed. Then find the volume.
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 16
Answer:
The volume of the figure is 4.166 ft3

Explanation:
Given,
l = 3\(\frac{1}{3}\) = \(\frac{10}{3}\)
w = 5 ft
h = \(\frac{1}{4}\)
Volume =  l × w × h
= \(\frac{10}{3}\) × 5 × \(\frac{1}{4}\)
= \(\frac{(10 × 5 × 1)}{(3 × 4}\)
= \(\frac{50}{12}\)
= \(\frac{25}{6}\)
= 4.166 ft3

Question 2.
Math on the Spot An aquarium is shaped like a rectangular prism. The prism is 24\(\frac{1}{4}\) inches long, 12\(\frac{1}{2}\) inches wide, and 20 inches high. What is the volume of the aquarium?
Answer:
The volume of the aquarium is 6062.5 in3

Explanation:
Given,
l = 24\(\frac{1}{4}\) = \(\frac{97}{4}\) inches
w = 12\(\frac{1}{2}\) inches =\(\frac{25}{2}\) inches
h = 20 inches
Volume of the aquarium = l × w × h
= \(\frac{97}{4}\) × \(\frac{25}{2}\) × 20
= \(\frac{(97 × 25 × 20}{8}\)
= \(\frac{48500}{8}\)
= 6062.5 in3

Question 3.
Reason Ray has 9 identical show boxes like the one shown. What is the total volume of all 9 shoe boxes?
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 17
Answer:
The volume of the figure is 976.5 in3

Explanation:
l = 15\(\frac{1}{2}\) = \(\frac{31}{2}\)
w = 12\(\frac{1}{2}\) = \(\frac{25}{2}\)
h = 6 in
volume of the figure = l × w × h
= \(\frac{31}{2}\) × \(\frac{25}{2}\) × 6
= \(\frac{3904}{4}\)
= 976.5 in3

For Problems 4-7, find the volume of each figure.

Question 4.
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 18
Answer:
Volume = \(\frac{1}{3375}\) ft3

Explanation:
Given,
l = \(\frac{1}{15}\)
w= \(\frac{1}{15}\)
h = \(\frac{1}{15}\)
Volume of the figure is l × w × h
Volume = \(\frac{1}{15}\) × \(\frac{1}{15}\) × \(\frac{1}{15}\)
= \(\frac{1}{3375}\) ft3

Question 5.
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 19
Answer:
Volume = 24806.5 in3

Explanation:
Given,
l = 35 in, w = 70 in and height = 10\(\frac{1}{8}\) = \(\frac{81}{8}\)
Volume of the figure is l × b × h
Volume = 35 × 70 × \(\frac{81}{8}\)
= 24806.5 in3

Question 6.
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 20
Answer:
The volume of the figure is 140.25 in3

Explanation:
Given,
l = 8\(\frac{1}{2}\) = \(\frac{17}{2}\)
w = 1\(\frac{1}{2}\) = \(\frac{3}{2}\)
h = 11 in
Volume of the figure is l × w × h
= \(\frac{17}{2}\) × \(\frac{3}{2}\) × 11
= \(\frac{(17 × 3 × 11)}{(2 × 2)}\)
= \(\frac{561}{4}\)
= 140.25 in3

Question 7.
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 21
Answer:
Volume of the figure is 2.25 m3

Explanation:
Given,
l = 1.5 m
w = 1.5 m
h = 1 m
Volume of the given figure is l × w × h
volume = 1.5 × 1.5 × 1
= 2.25 m3.

Test Prep

Question 8.
Anton is filling a fish tank with water. What volume of water does he need?
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 22
(A) 19,125 in3
(B) 18,375 in3
(C) 4,815 in3
(D) 90\(\frac{1}{2}\) in3
Answer:
Volume of water = 19125 in3

Explanation:
Given,
l = 50 in
w = 15 in
l = 25\(\frac{1}{2}\) = \(\frac{51}{2}\)
Volume of the water = l × w × h
volume = 50 × 15 × \(\frac{51}{2}\)
= 19125 in3

Question 9.
Jordan needs to carry drinking water to help people in a flooded area. One jug has the dimensions shown.
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 23
What is the volume of one jug of drinking water?
Answer:
Volume of jug of drinking water =\(\frac{1}{30}\) = 0.33 cubic ft.

Explanation:
Given,
l = \(\frac{1}{3}\)
w = \(\frac{1}{5}\)
h = \(\frac{1}{2}\)
volume = l × w × h
v = \(\frac{1}{3}\) × \(\frac{1}{5}\) × \(\frac{1}{2}\)
v = \(\frac{1}{30}\)
Volume of jug of drinking water =\(\frac{1}{30}\) = 0.33 cubic ft.

Spiral Review

Question 10.
42 is 60% of what number?
Answer:
42 × \(\frac{60}{100}\)
25.2

Question 11.
Tyrell buys an organizer for his baseball cards that costs $12.99. He can add pages to the organizer to hold the cards. Each page costs $2.75 and holds 9 cards. If Tyrell has 100 cards, how much will it cost him to organize them? Write and evaluate a numeric expression.
Answer:

Question 12.
Greg has a goal to read 529 pages of a book in 6 days. The number of pages he read on the first 3 days is given in the table. Write and solve an equation to find the number of pages, p, Greg has left to read.
HMH Into Math Grade 6 Module 13 Lesson 2 Answer Key Find Volume of Rectangular Prisms 24
Answer:
The number of pages Greg has left to read is 210.

Explanation:
Greg has to read 529 pages.
The number of pages he read on the first day is 110+ 92 +117 = 319
Therefore the number of pages Greg has left to read is 529 – 319 = 210

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