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.

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.

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.

What is the volume of one small cube? cubic unit(s)

Answer:

D. Complete the model.

What b the edge length of one small cube? 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.

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.

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

Answer:

C. Josh’s container can hold in^{3} of flour.

Answer:

Josh’s container holds 850 in^{3} 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.

Answer:

The volume of the rectangular prism is 10.56 in^{3}.

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 in^{3}.

Question 2.

What is the volume of a rectangular prism that has a base area of \(\frac{1}{8}\) in^{2} and a height of \(\frac{3}{4}\) in.?

Answer:

Given,

B = Area = \(\frac{1}{8}\) in^{2}

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?

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.

Answer:

Volume = (l × w × h) – w^{3}

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

Question 5.

Answer:

The volume of the cube = 343 cm^{3}

Explanation:

Given,

a = 7 cm

Volume of the cube = a^{3}

= 7 × 7 × 7

= 343 cm^{3}

Question 6.

Answer:

The volume of the figure is 126299.25 in^{3}

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 in^{3}

Question 7.

Answer:

The volume of the figure is 1710 ft^{3}

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 ft^{3}

Question 8.

Answer:

The volume of the figure is 33.64 ft^{3}

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 ft^{3}

**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.

Answer:

The volume of the figure is 4.166 ft^{3}

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 ft^{3}

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 in^{3}

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 in^{3}

Question 3.

**Reason** Ray has 9 identical show boxes like the one shown. What is the total volume of all 9 shoe boxes?

Answer:

The volume of the figure is 976.5 in^{3}

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 in^{3}

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

Question 4.

Answer:

Volume = \(\frac{1}{3375}\) ft^{3}

Explanation:

Given,

l = \(\frac{1}{15}\)

w= \(\frac{1}{15}\)

h = \(\frac{1}{15}\)

Volume of the figure is l × w × h

Volume = \(\frac{1}{15}\) × \(\frac{1}{15}\) × \(\frac{1}{15}\)

= \(\frac{1}{3375}\) ft^{3}

Question 5.

Answer:

Volume = 24806.5 in^{3}

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 in^{3}

Question 6.

Answer:

The volume of the figure is 140.25 in^{3}

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 in^{3}

Question 7.

Answer:

Volume of the figure is 2.25 m^{3}

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 m^{3}.

**Test Prep**

Question 8.

Anton is filling a fish tank with water. What volume of water does he need?

(A) 19,125 in^{3}

(B) 18,375 in^{3}

(C) 4,815 in^{3}

(D) 90\(\frac{1}{2}\) in^{3}

Answer:

Volume of water = 19125 in^{3}

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 in^{3}

Question 9.

Jordan needs to carry drinking water to help people in a flooded area. One jug has the dimensions shown.

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.

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