If the side of a cube
is an integer, which
of the following can
be the volume of the
cube in cubic units?
Answers
Answer:
In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 23 = 8 or (x + 1)3.
y = x3 for values of 1 ≤ x ≤ 25.
The cube is also the number multiplied by its square:
n3 = n × n2 = n × n × n.
The cube function is the function x → x3 (often denoted y = x3) that maps a number to its cube. It is an odd function, as
(−n)3 = −(n3).
The volume of a geometric cube is the cube of its side length, giving rise to the name. The inverse operation that consists of finding a number whose cube is n is called extracting the cube root of n. It determines the side of the cube of a given volume. It is also n raised to the one-third power.
The graph of the cube function is known as the cubic parabola. Because cube is an odd function, this curve has a center of symmetry at the origin, but no axis of symmetry.
Step-by-step explanation:
Expii
Pre-AlgebraCube Roots
Perfect Cubes — Definition & Examples
A perfect cube can be broken down to an integer multiplied by itself three times. For example, 3x3x3=27, so 27 is a perfect cube.
Perfect Cubes — Definition & Examples
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Explanations (4)
Alex Federspiel
Text
8
Perfect Cube
To understand what a perfect cube is, it's helpful to look at a few shapes. Specifically, the name "perfect cubes" suggest we consider cubes from geometry.
A cube is just a three dimensional square. Every side has the same length. A common example of a cube is a die, like you would use when playing Yahtzee.
A cube.
If one side of the cube has a length of
5
, then every side of the cube has a length of
5
. Believe it or not, each cube has
12
sides. It is made out of six squares, which are called faces.
A cube with length 5.
To find the volume of a cube, we multiply the length, width, and height together. According to the order of operations, we multiply from left to right
V
=
l
×
w
×
h
V
=
5
×
5
×
5
V
=
25
×
5
V
=
125
For simplicity we have omitted any units. Some possible options are centimeters, meters, and kilometers.
We refer to
125
as a perfect cube because it's the product of an integer multiplied by itself three times,
5
×
5
×
5
. In other words, the cube root of 125 is
5
. A cube root can also be written as a fractional exponent:
3
√
125
=
125
1
3
.
By multiplying other integers together with themselves, we can find other perfect cubes.
1
×
1
×
1
=
1
2
×
2
×
2
=
8
3
×
3
×
3
=
27
4
×
4
×
4
=
64
5
×
5
×
5
=
125
6
×
6
×
6
=
216
7
×
7
×
7
=
343
8
×
8
×
8
=
512
9
×
9
×
9
=
729
10
×
10
×
10
=
1,000
There are infinitely many perfect cubes. Find the cube of any integer you want, and you've found yourself another perfect cube! For some of the bigger ones, you might want a calculator to find them. However, it's worth memorizing the ten we listed above.