All the solutions provided in McGraw Hill My Math Grade 5 Answer Key PDF Chapter 12 Lesson 8 Use Models to Find Volume will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 5 Answer Key Chapter 12 Lesson 8 Use Models to Find Volume
Volume is the amount of space inside a three-dimensional figure. Centimetre cubes can help you find the volume of a prism.
Build It
Use centimeter cubes to build four different rectangular prisms.
Complete the fourth and fifth columns of the table below for each prism.
A prism built from cubes has no gaps or overlaps.
A cube with a side length of one unit is called a unit cube.
A unit cube has a volume of 1 cubic unit or 1 unit3.
A cubic unit is a unit for measuring volume.
So, if you use 12 centimeter cubes to build a rectangular prism, the prism has a volume of ______________ cubic centimeters, or _____________ cm3.
Answer:
Formula:
The volume of the rectangular prism = length x width x height
V = 1 x 2 x 1 = 1
V = 2 x 2 x 1 = 4
V = 3 x 2 x 2 = 12
V = 4 x 2 x 2 = 16 cubic centimetres.
So, if you use 12-centimeter cubes to build a rectangular prism, the prism has a volume of 12 cubic centimetres or 12 cm^3.
Try It
Use centimeter cubes to build the rectangular prism shown. Complete the table for each layer.
How many cubes were used to build the prism? ______________
What is the volume? ______________
Answer:
In the above-given figure, length; width; height is given.
length = 4
width = 3
height = 1
from the measurements, we can easily find out the volume.
We know that the volume of the rectangular prism = length x width x height
V(layer 1) = 4 x 3 x 1 = 12
V(layer 2) = 4 x 3 x 1 = 12
V(layer 3) = 4 x 3 x 1 = 12
V(layer 4) = 4 x 3 x 1 = 12
The number of cubes used to build = 12 x 4 = 48 cubic centimetres.
Therefore, the volume is 48 cm^3.
Talk About It
Question 1.
Describe the relationship between the number of cubes needed to build a rectangular prism and its volume, in cubic units.
Answer:
The volume of a unit cube whose length, width and height are 1 unit each is 1 cubic unit. Here, the rectangular prism is made up of smaller unit cubes. The length, width and height of the rectangular prism can be measured by counting the number of unit cubes.
From the above information, we can conclude that:
– The volume is the same as the number of cubes needed to build a rectangular prism.
Question 2.
Describe the pattern in the table between the length, width, and height. and volume of each prism.
Answer:
The pattern in the table:
The product of length, width, and height.
We know that the volume of the rectangular prism = length x width x height.
Question 3.
Use l for length, w for width, and h for height to write a formula for the volume V of a rectangular prism.
Answer:
– “l” is the base length
– “w” is the base width
– “h” is the height of the prism
To find the volume of the rectangular prism, we multiply the length, width, and height, that is the area of the base multiplied by the height. It should be noted that the volume is measured in cubic units.
The volume of the rectangular prism = l x w x h
Question 4.
Mathematical PRACTICE Use Math Tools Use your formula to find the volume of the prism at the right in appropriate units. Verify your solution by counting the number of cubes.
Answer:
To find the volume of the rectangular prism, we multiply the length, width, and height, which is the base’s area multiplied by the height. It should be noted that the volume is measured in cubic units.
The volume of the rectangular prism = length x width x height
length = 4; width = 2; height = 3
V = 4 x 2 x 3
V = 24 cubic units
Practice It
Mathematical PRACTICE Use Math Tools Use centimetre cubes to build the rectangular prism shown.
Question 5.
Complete the table below.
Answer:
We know that the formula for the rectangular prism:
The volume of the rectangular prism = length x width x height
length = 4 ; width = 4; height = 1
V(layer 1) = 4 x 4 x 1 = 16
V(layer 2) = 4 x 4 x 1 = 16
Question 6.
How many cubes were used to build the prism? ____________
What is the volume? _____________ cm3
Answer:
The number of cubes used to build the prism = 16 x 2 = 32 cubes
(or) we can add 16 + 16 = 32 cubes.
Therefore, the volume of the prism = 32 cubic centimetres.
Use centimeter cubes to build the rectangular prism shown.
Question 7.
Complete the table below.
Answer:
We know that the formula for the rectangular prism:
The volume of the rectangular prism = length x width x height
length = 6 ; width = 3; height = 1
V(layer 1) = 6 x 3 x 1 = 18
V(layer 2) = 6 x 3 x 1 = 18
V(layer 3) = 6 x 3 x 1 = 18
V(layer 4) = 6 x 3 x 1 = 18
Question 8.
How many cubes were used to build the prism? ____________
What is the volume? _____________ cm3
Answer:
The number of cubes used to build the prism = 18 x 4 = 72 cubes
(or) we can add 18 + 18 + 18 + 18 = 72 cubes.
The volume of the prism = 72 cubic centimetres.
Apply It
Use the prism shown for Exercises 9-11.
Question 9.
What shape is the base of the prism?
Answer:
– It has 6 faces (all are rectangular),12 sides, and 8 vertices.
– It is a rectangular prism.
– For a rectangular prism, the base is always a rectangle.
Question 10.
Mathematical PRACTICE Explain to Friend Explain to a friend how to find the area of the base of the prism.
Answer:
– In a Rectangular Prism, 2 rectangular bases are parallel to each other and 4 rectangular faces.
– The base area of a rectangular prism formula = base length x base width.
Question 11.
Find the volume of the prism above by multiplying the area of the base by the height. Verify your solution by counting the number of centimetre cubes.
Answer:
To find the volume of the rectangular prism, we multiply the length, width, and height, which is the base’s area multiplied by the height. It should be noted that the volume is measured in cubic units.
The volume of the rectangular prism = length x width x height
(refer to the above prism question 9)
for the above-given prism, the length is 5; the width is 3; the height is 3.
Now substitute the values in the formula:
V = 5 x 3 x 3
V = 45
Therefore, the volume of the rectangular prism is 45 cubic centimetres.
Question 12.
Mathematical PRACTICE Make Sense of Problems Valerie knows that the volume of a prism is 36 cubic units. She knows that the length of the prism is 4 units and the width is 3 units. What is the height of the prism?
Answer:
The above-given:
The volume of the prism = 36
The length of the prism = 4
The width of the prism = 3
The height of the prism = h
We know that the volume of the rectangular prism = length x width x height
V = l x w x h
36 = 4 x 3 x h
36 = 12 x h
36 / 12 = h
3 = h
Therefore, the height of the prism is 3 units.
Write About It
Question 13.
Describe a way to find the volume of a rectangular prism without using models.
Answer:
– We can find the volume of a rectangular prism by multiplying the length, width, and height (or)
– The volume of a rectangular prism is the capacity that it can hold or the space occupied by it. Thus, the volume of a rectangular prism can be calculated by multiplying its base area by its height. The formula that is used to find the volume of a rectangular prism is, Volume (V) = height of the prism × base area.
McGraw Hill My Math Grade 5 Chapter 12 Lesson 8 My Homework Answer Key
Vocabulary Check
Fill in each blank with the correct term or number to complete each sentence.
Question 1.
Volume is the amount of ______________ inside a three-dimensional figure.
Answer: space
Volume is the amount of space occupied by the object or figure in three-dimensional space.
Question 2.
A cube with a side length of _______________ unit is called a unit cube.
Answer: one
a unit cube is a three-dimensional object. It also has 12 edges. And, the major point to be focussed on is that the length of all edges is equal to 1 unit. A unit cube is also called a ‘Cube of Side 1’. It has six faces which are unit squares.
Question 3.
The volume of a rectangular prism can be found by multiplying the length by the ______________ by the height.
Answer: width.
To find the volume of the rectangular prism, we multiply the length, width, and height, which is the base’s area multiplied by the height. It should be noted that the volume is measured in cubic units.
The volume of the rectangular prism = length x width x height
Practice
For Exercises 4-7, centimeter cubes were used to build the rectangular prism shown.
Question 4.
How many cubes were needed to build Layer 1?
Answer:
Length of layer 1 = 4
width of layer 1 = 2
height of layer 1 = 1
The volume = 4 x 2 x 1
V = 8 cubes
Therefore, the number of cubes needed to build layer 1 is 8.
Question 5.
Complete the table below.
Answer:
We know that the formula for the rectangular prism:
The volume of the rectangular prism = length x width x height
length = 4 ; width = 2; height = 1
V(layer 1) = 4 x 2 x 1 = 8
V(layer 2) = 4 x 2 x 1 = 8
V(layer 3) = 4 x 2 x 1 = 8
V(layer 4) = 4 x 2 x 1 = 8
V(layer 5) = 4 x 2 x 1 = 8
Question 6.
How many cubes were used to build the prism?
Answer:
The number of cubes used to build the prism = 8 x 5 = 40 (or)
8 + 8 + 8 + 8 + 8 = 40
Therefore, 40 cubes are needed to build the prism.
Question 7.
What is the volume of the prism?
Answer:
The volume of the prism = base area x height
V = 8 x 5
V = 40 cubic centimetres
Therefore, the volume of the prism is 40 cubic centimetres.
Problem Solving
Question 8.
Mathematical PRACTICE Make Sense of Problems Samir knows that the volume of a prism is 40 cubic units. He also knows that the width of the prism is 2 units and the height is 5 units. What ¡s the length of the prism?
Answer:
The above-given:
The volume of the prism = 40
The width of the prism = 2
The height of the prism = 5
The length of the prism = l
We know that the formula for the rectangular prism:
The volume of the rectangular prism = length x width x height
Substitute the values in the prism:
40 = l x 2 x 5
40 = l x 10
40 / 10 = l
4 = l
Therefore, the length of the prism is 40 cubic units.
Question 9.
Centimetre cubes were used to build the prism. What is the volume of the prism?
Answer:
To find the volume of the rectangular prism, we multiply the length, width, and height, which is the base’s area multiplied by the height. It should be noted that the volume is measured in cubic units.
The volume of the rectangular prism = length x width x height
length = 6; width = 3; height = 3
V = 6 x 3 x 3
V = 54
Therefore, the volume of the prism is 54 cubic units.