Area measures how much space there is on a flat surface. In this lesson, we'll learn about the various measurement units of area and how they relate to units of length.
Consider a square with sides of length shown below.
To find the area of a square, we multiply its side lengths. Therefore, the area of this square is equal to
The unit of area we used is called a square meter. In this case, we say that the area of our square is one square meter.
In previous lessons, we learned that length can also be measured in kilometers centimeters and millimeters Each of these length units has a corresponding area unit:
A square with sides of length has an area of or one square kilometer.
A square with sides of length has an area of or one square centimeter.
A square with sides of length has an area of or one square millimeter.
The same idea applies when measuring area in customary units. For example:
A square with sides of length has an area of or one square inch.
A square with sides of length has an area of or one square foot.
Volume measures how much three-dimensional space there is inside something.
Consider a cube with sides of length shown below.
To find the volume of a cube, we multiply its side lengths. Therefore, the volume of this cube is equal to
The unit of volume we used is called a cubic meter. In this case, we say that the volume of our cube is one cubic meter.
As with area, each unit of length has a corresponding volume unit. For example:
A cube with sides of length has a volume of or one cubic centimeter.
A cube with sides of length has a volume of or one cubic inch.
Suppose we want to measure the volume of a shoe box. What units could we use?
We can measure length in centimeters When measuring lengths in centimeters, volumes are measured in which is usually written as
Therefore, the correct answer is "II only."
Suppose we want to measure the area of the school playground. What units could we use?
|
a
|
$\textrm{m}$ |
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b
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$\textrm{m}^3$ |
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c
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$\textrm{s}$ |
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d
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$\textrm{m}^2$ |
|
e
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$\textrm{kg}^2$ |
Suppose we want to measure the volume of a fish tank. What units could we use?
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a
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$\textrm{in}^3$ |
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b
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$\textrm{in}$ |
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c
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$\textrm g^2$ |
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d
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$\textrm s$ |
|
e
|
$\textrm{in}^2$ |
A square is a special type of rectangle whose length and width are equal. For example, consider the square below.
We say that the side length of this square equals
Since a square is a special type of rectangle, we find its area by multiplying its length and width. However, since its length and width are equal, we can find its area by squaring its side length:
Therefore, the area of the square is
What is the area of the square above?
To calculate the area of a square, we square its side length. Therefore, the area of the square is
What is the area of the square above?
|
a
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$36 \,\textrm{mm}^3$ |
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b
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$36 \,\textrm{mm}^2$ |
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c
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$16 \,\textrm{mm}^2$ |
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d
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$36 \,\textrm{mm}$ |
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e
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$16 \,\textrm{mm}$ |
If a square has a side length of $11 \, \textrm{in},$ what is its area?
|
a
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$44 \, \textrm{in}$ |
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b
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$44 \, \textrm{in}^2$ |
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c
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$121 \, \textrm{in}^2$ |
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d
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$121 \, \textrm{in}^3$ |
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e
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$121 \, \textrm{in}$ |
A cube is a special type of rectangular solid whose length, width, and height are equal.
We say that the side length of this cube equals
Since a cube is a special type of rectangular solid, we find its volume by multiplying its length, width, and height. However, since its length, width, and height are all equal, we can find its volume by cubing its side length:
What is the volume of the cube shown in the diagram above?
To find the volume of a cube, we cube its side length. Therefore,
What is the volume of the cube shown in the diagram above?
|
a
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$216 \,\textrm{mm}^2$ |
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b
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$1\,296 \,\textrm{mm}^2$ |
|
c
|
$216 \,\textrm{mm}^3$ |
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d
|
$216 \,\textrm{mm}$ |
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e
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$1\,296 \,\textrm{mm}^3$ |
A cube has a side length of $3\,\textrm{ft}.$ What is the volume of the cube?
|
a
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$27\,\textrm{ft}^3$ |
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b
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$18\,\textrm{ft}$ |
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c
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$18\,\textrm{ft}^3$ |
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d
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$27\,\textrm{ft}$ |
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e
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$27\,\textrm{ft}^2$ |