ID : ae-8-Cubes-and-Cube-Root [1]
Grade 8
Cubes and Cube Root
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Answer the questions
(1)
Which of the following numbers is not a perfect cube?
39304, 12167, 10648, 4914
(2)
Solve the following:
(3)
Find the value of A if
(4)
Solve the following :
(5)
A cubical box has all sides of 39 m. What is its volume?
(6)
If one face of a cube has an area of 225 m 2, then what is the volume of the cube?
(7)
If you have a container in the shape of a cube that has a volume of 216 m 3, then what is the area
of each of the faces of the cube?
Choose correct answer(s) from given choice
(8)
(9)
Which of the following statements is false:
a. Cubes of even numbers are always even
b. Cubes of odd numbers are always odd
c. 45360 is a perfect cube
d. 41650 is not a perfect cube
Which of the following choices is the value of
.
a. 12
b. -2
c. 3
d. 5
(10) Which of the following choices is the cube root of 4096
a. 7
b. 16
c. 22
d. 27
(11) What is the value of
a.
c.
169
27
13
27
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.
b.
d.
13
26
13
729
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ID : ae-8-Cubes-and-Cube-Root [2]
(12) Take a number x, and multiply it with 2. Take the cube of the resulting number. What is the ratio of
this number to the cube of the original number?
a. 8:1
b. 4:1
c. 2:1
d. 8:2
(13) A number n is called a perfect cube if there exists:
a. a natural number m such that n = m x m
b. a natural number m such that n = m x m x m
c. a natural number m such that m = n + n + n
d. a natural number m such that m = n x n x n
Fill in the blanks
(14)
(15)
The cube root of 58 correct to one place of decimal is
The value of
is
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ID : ae-8-Cubes-and-Cube-Root [3]
Answers
(1)
4914
(2)
-420
(3)
5
(4)
1953125
(5)
59319 m 3
Step 1
We know that the volume of a cube (or a cubical box) is calculated by taking the cube of its
side.
Step 2
We have been told that the side of the cube in question is 39 m. Therefore, its volume = (39)3
m3
= 39 × 39 × 39 m 3
= 59319 m 3
Step 3
Therefore, the volume of the cubical box is 59319 m3.
(6)
3375 m 3
(7)
36 m 2
Step 1
Let us assume the side of a cube shape container is a.
Step 2
Volume of cube = 216 m 3
also, volume of the cube = a3
compare both, a3 = 216
⇒ a = (216)
1
3
⇒a=6
Step 3
Area of side of the cube = a2
= 62
= 36
Step 4
Therefore, the area of the face of cube shape container is 36 m2.
(8)
c. 45360 is a perfect cube
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ID : ae-8-Cubes-and-Cube-Root [4]
(9)
d. 5
(10) b. 16
(11)
c.
13
27
Step 1
We have been asked to find the value of
.
Step 2
Now,
=(
(13)3
=(
)
(27)3
= ((
=
13
27
)3)
(13 × 13 × 13)
(27 × 27 × 27)
)
1
3
1
3
1
3
13
27
Step 3
Therefore, the value of
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is
13
27
.
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ID : ae-8-Cubes-and-Cube-Root [5]
(12) a. 8:1
Step 1
If we multiply the number x with 2, the resulting number is: 2x.
Step 2
The cube of the resulting number 2x = (2x)3
= 8x3
Step 3
The original number is x.
Cube of the original number = x3.
Step 4
The ratio of the new number to the original number =
=
New number
Original number
8x3
x3
=
8
1
Step 5
Therefore, the ratio of the new number to the cube of the original number is 8:1.
(13) b. a natural number m such that n = m x m x m
Step 1
A perfect cube is a natural number that has a natural number as its cube root.
In other words, a perfect cube is the result of multiplying a natural number three times by
itself.
For example: 5 × 5 × 5 = 53 = 125, which is a perfect cube.
Step 2
For any natural number m, n = m × m × m is a perfect cube.
Step 3
Therefore, the number n is called a perfect cube if there exists a natural number m such that
n = m × m × m.
(14)
(15)
3.9
0.46
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