This handy Math in Focus Grade 5 Workbook Answer Key Cumulative Review Chapters 14 and 15 provides detailed solutions for the textbook questions.

## Math in Focus Grade 5 Cumulative Review Answer Key for Chapters 14 and 15

**Concepts and Skills**

**Name each solid. Then write the number of faces and vertices, and the shapes of the faces. (Lesson 14.1)**

Question 1.

Answer:

Explanation:

Given solid triangular prism shape has number of faces -4,

number of vertices-6 and shapes of faces- 8.

Question 2.

Answer:

Explanation:

Given solid triangular prism shape has number of faces – 5,

number of vertices – 5 and shapes of faces – 10.

**Name the solid formed from each net. (Lesson 14.1)**

Question 3.

Answer:

Explanation:

Given solid formed with the net is pentagonal prism.

Question 4.

Answer:

Explanation:

Given solid formed with the net is square based pyramid.

**Complete. (Lesson 14.2)**

Question 5.

A ___ has two parallel and congruent bases that are joined by a curved surface.

Answer:

Cylinder,

Explanation:

A cylinder is formed by two parallel congurent circular bases and a curved surface that connects

the bases.

Question 6.

A ____ does not have any edges or vertices, and has the same distance

across any line through its center.

Answer:

Circle,

Explanation:

A circle does not have any edges or vertices, and has the same distance

across any line through its center.

Question 7.

A _____________ has one vertex, a circular base, and a curved surface.

Answer:

Cone,

Explanation:

A cone has one vertex, a circular base, and a curved surface.

Question 8.

A sphere has no ___ and________ surfaces.

Answer:

Faces, Edges, Vertices,

Explanation:

A sphere has no faces, edges, vertices and surfaces.

**Find how many unit cubes are used to build each solid. (Lesson 15.1)**

Question 9.

_____________ unit cubes

Answer:

16 unit cubes,

Explanation:

As a cube has all its sides of the same length.

A unit cube has all its sides of length 1 unit.

we have 16 unit cubes,

So, the volume of a 16 unit cubes = 16 X (Side × Side × Side),

= 16 X (1 unit × 1 unit × 1 unit),

= 16 unit cubes.

Question 10.

_____________ unit cubes

Answer:

13 unit cubes,

Explanation:

As a cube has all its sides of the same length.

A unit cube has all its sides of length 1 unit.

we have 13 unit cubes,

So, the volume of a 13 unit cubes = 13 X (Side × Side × Side),

=13 X (1 unit × 1 unit × 1 unit),

= 13 unit cubes.

**Draw a cube with edges 2 times as long as the edges of this unit cube. (Lesson 15.2)**

Question 11.

Answer:

Explanation:

As a cube has all its sides of the same length.

A unit cube has all its sides of length 1 unit.

Shown the volume of a unit cube = Side × Side × Side,

= 2 units × 1 unit × 1 unit,

= 2 units cubes.

**Complete the drawing of this rectangular prism. (Lesson 15.2)**

Question 12.

Answer:

Explanation:

Drawn one rectangular prism on the dot paper,

As given rectangular prism has 4 units X 2 units X 3 units =

24 unit cubes rectangular prism.

**Find the surface area of each prism. (Lesson 15.3)**

Question 13.

Answer:

The surface area of rectangular prism is 1860 cm^{2},

Explanation:

As the surface area of rectangular prism is

2 X [(width X length) + (height X length) + (height X width)],

= 2 X [(18 cm X 20 cm) + (20 cm X 15 m) + (15 cm X 18 cm)],

= 2 X [(360 cm^{2}) + (300 cm^{2}) + (270 cm^{2})]

= 2 X [ 930 cm^{2}],

= 1860 cm^{2}.

Question 14.

Answer:

Surface area of triangular prism = 1,392 cm^{2},

Explanation:

2 × \(\frac{1}{2}\) × 12 cm × 16 cm = 192 cm^{2},

12 cm × 25 cm = 300 cm.^{2
}16 cm × 25 cm = 400 cm.^{2
}20 cm × 25 cm = 500 cm.^{2
}192 cm ^{2}+ 300 cm^{2} + 400 cm^{2} + 500 cm.^{2} = 1,392 cm^{2},

Surface area of triangular prism = 1,392 cm^{2}.

**These solids are built using 1-inch cubes. Find and compare their volumes. (Lesson 15.4)**

Question 15.

Length = _____4_______ in.

Width = _____4_______ in.

Height = _____4______ in.

Volume = _____64_____ in.^{3}

Length = ______6______ in.

Width = _______4_____ in.

Height = ______3_____ in.

Volume = _____72_____ in.^{3}

Solid _______A____ has less volume than solid ____B______.

Answer:

Volume of given cube A has 64 cubic units,

Volume of given cube B has 72 cubic units,

Solid A has less volume than solid B,

Explanation:

As we know volume of solid is l X w X h,

Total surface area of A is 4 in X 4 in X 4 in = 64 cubic units.

Total surface area has 6 in X 4 in X 3 in = 72 cubic units.

Given cube contains 2 less small unit cubes so first we

calculate total surface and subtract missing cubic uints,

therefore, Solid A has less volume than solid B,

**Find the volume of each rectangular prism. (Lesson 15.5)**

Question 16.

Answer:

Volume of given rectangular prism is 27 cm^{3},

Explanation:

Given Length = 3 cm, Width = 1 cm and Height = 9 cm,

Volume of the rectangular prism is lwh = 3 cm X 1 cm X 9 cm = 27 cm^{3}.

Question 17.

Answer:

Volume of given rectangular prism is 330 m^{3},

Explanation:

Given Length = 11 m, Width = 6 m and Height =5 m,

Volume of the rectangular prism is lwh = 11 cm X 6 m X 5 m = 330 m^{3}.

**Find the volume of water in each container in liters and milliliters. (Lesson 15.5)**

Question 18.

Answer:

Volume of given rectangular prism is 10,290 cm^{3 }which is equal to 10,290 milliliters,

Explanation:

Given Length = 14 cm, Width = 21 cm and Height = 35 cm,

Volume of the rectangular prism is lwh = 14 cm X 21 cm X 35 cm = 10,290 cm^{3}.

as 1 cubic centimeter is equal to 1 milliliters therefore volume of given

rectangular prism is 10,290 cm^{3 }which is equal to 10,290 milliliters.

Question 19.

Answer:

Volume of given rectangular prism is 1,008 cm^{3 }which is equal to 1,008 milliliters,

Explanation:

Given Length = 7 cm, Width = 9 cm and Height = 16 cm,

Volume of the rectangular prism is lwh = 7 cm X 9 cm X 16 cm = 1,008 cm^{3}.

as 1 cubic centimeter is equal to 1 milliliters therefore volume of given

rectangular prism is 1,008 cm^{3 }which is equal to 1,008 milliliters.

**Problem Solving**

**Solve. Show your work.**

Question 20.

The length of a rectangular block is 20 inches. Its width is half its length.

Its height is half its width. What is the surface area of the block?

Answer:

The surface area of a rectangular prism is 1860 cm^{2},

Explanation:

Given the length of a rectangular block is 20 inches. Its width is half its length.

So width is 10 inches, Its height is half its width is 5 inches

The surface area of the block is

2 X [(width X length) + (height X length) + (height X width)],

= 2 X [(10 in X 20 in) + (5 in X 20 in) + (5 in X 10 in)],

= 2 X [(200 in^{2}) + (100 in^{2}) + (50 in^{2})]

= 2 X [ 350 in^{2}],

= 700 in^{2}.

**Solve. Show your work.**

Question 21.

A rectangular piece of poster board measures 70 centimeters by 50 centimeters.

The net of a cube with 12-centimeter edges is cut from it.

What is the area of the poster board left?

Answer:

The area of the poster board left 2,636 cm^{2},

Explanation:

Given a rectangular piece of poster board measures 70 centimeters by 50 centimeters,

70 cm X 50 cm = 3,500 cm^{2}, The net of a cube with 12-centimeter edges is cut from it.

Volume of cube is 6 X 12 cm X 12 cm = 864 cm^{2}, therefore the area of the poster board

left is 3,500 cm^{2} – 864 cm^{2 }= 2,636 cm^{2}.

Question 22.

A rectangular prism is 15 inches long and 12 inches high.

Its width is \(\frac{3}{5}\) its length. Find its volume.

Answer:

Volume of a rectangular prism is 1,620 in^{3},

Explanation:

Given a rectangular prism is 15 inches long and 12 inches high.

Its width is \(\frac{3}{5}\) its length. So length is

\(\frac{3}{5}\) X 15 = \(\frac{3 X 15}{5}\) = 9 inches,

therefore volume is 15 inches X 12 inches X 9 inches = 1,620 in^{3}.

**Solve. Show your work.**

Question 23.

Three cubes with edges measuring 5 inches are stacked on top of one another.

What is the total volume of the 3 cubes?

Answer:

The total volume of the 3 cubes is 375 in^{3},

Explanation:

Given three cubes with edges measuring 5 inches are stacked on top of one another.

3 X (5 inches X 5 inches X 5 inches) = 3 X (125 in^{3}) = 375 in^{3}.

Question 24.

The rectangular container shown contains 2 liters of water.

How much more water must be added to fill the container completely?

Give your answer in liters.

Answer:

1,750 cubic cm more water must be added to fill the container completely,

Explanation:

Given rectangular cuboid volume is 10 cm X 25 cm X 15 cm = 3,750 cubic cms as

the rectangular container shown contains 2 liters of water.

Equal to 2 X 1000 = 2,000 cubic cms so much more water must be

added to fill the container completely is 3,750 cubic cm – 2,000 cubic cm = 1,750 cubic cm.

**Solve. Show your work.**

Question 25.

A container is 28 centimeters long, 1 4 centimeters wide, and 10 centimeters high.

It is half-filled with juice. Kathy pours 500 milliliters of water into the

container to make a juice drink. Find the volume of juice drink in the container now.

Give your answer in liters and milliliters.

Answer:

Given a container is 28 centimeters long, 1 4 centimeters wide, and 10 centimeters high.

Volume of container is 28 cm X 14 cm X 10 cm = 3,920 cubic centimeters,

It is half-filled with juice. \(\frac{1}{2}\) X 3,920 = 1,960 cubic centimeters or

1,960 milliliters now Kathy pours 500 milliliters of water into the container

to make a juice drink. Therefore the volume of juice drink in the container now is

1,960 milliliters + 500 milliliters = 2,460 milliliters and 1,000 milliliters = 1 liter,

So 2 L 460 milliliters.

Question 26.

The fish tank shown is filled with 4 liters of water per minute from a faucet.

How long does it take to fill the tank completely?

Answer:

Long does it will take to fill the tank completely is 6 minutes,

Explanation:

Given the tank has length is 45 cm, width is 16 cm and height is 30 cm,

volume = 45 cm X 16 cm X 30 cm = 2,16,00 cubic cms 21 liters 600 milliliters,

as fish tank shown is filled with 4 liters of water per minute from a faucet,

Long does it will take to fill the tank completely is 21,600 ÷ 4 = 5 minutes 400 ≈ 6 minutes.

**Solve. Show your work.**

Question 27.

A tank with a square base with edges measuring 20 centimeters and a

height of 36 centimeters is \(\frac{2}{3}\)-filled with water.

Each minute, 2 liters of water leak out of the tank through a crack in the bottom.

How long does it take for all the water to leak out?

Answer:

It will be approximately 5 minutes long for water to leak out,

Explanation:

Given a tank with a square base with edges measuring 20 centimeters

and a height of 36 centimeters, So volume is

20 cm X 20 cm X 36 cm = 14,400 cubic centimeters ,

and tank is filled with \(\frac{2}{3}\)-filled with water means

\(\frac{2}{3}\) X 14,400 = 9,600 milliliters and each minute 2 liters of

water leak out of the tank through a crack in the bottom is

9,600 ÷ 2,000 = 4.8 **≈ **5minutes.

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