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Published on: 31/07/2019
Cubes and Cube Roots
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Questions + Answers key
Take MCQ Mathematics Test
1.
Which of the following are the cubes of even numbers?
(a) 32768
(b) 2744
(c) 2197
(d) 42875
(e) 132651
(f) 21952
2.
Which of the following are the cubes of odd numbers?
(a) 1331
(b) 4096
(c) 5832
(d) 8000
(e) 3375
(f) 4913
3.
Hardy-Ramanujan number 1729 is the smallest Hardy-Ramanujan number. There are infinitely many such numbers. Few are 4104 (2,16; 9,15), 13832 (18, 20; 2, 24). Check it with the numbers given in the brackets.
4.
Is 2744 a perfect cube?
5.
The cube of a two digits number may be a three digits number.
6.
There is no perfect cube which ends with 8.
7.
If square of a number ends with 5, then its cube ends with 25.
8.
A perfect cube does not end with two zeroes.
9.
Cube of any odd number is even.
10.
Show that 46656 is a perfect cube.
11.
Evaluate {52+(122)1/2}3
12.
If the digit in ones place of number is 6, then its cube will end with the digits:
6
3
2
none of these.
13.
If the digit in ones place of a number is 3, then the ending of its cube will be:
3
6
7
9
14.
Which of the following is the cube of an even natural number?
1331
4913
3375
1728
15.
The cube of 0.08 is
0.000512
0.0512
0.512
5.12
16.
The one's digit of the cube of 23 is
3
6
7
17.
Cube of a number ending in 7 will end in the digit ______
18.
The least number by which 72 is divided to make it a perfect cube is _____
19.
The least number by which 250 is multiplied to make it a perfect cube is _____
20.
The cube root of a number x is denoted by ______
21.
(1.2)3 = ______
22.
There are_____________ perfect cubes from 1 to 1000.
23.
The volume of a cubical box is 64cm3. Its side is________cm.
24.
Each prime factor of a perfect cube appear _________times in its cube
25.
\((\sqrt [ 3 ]{ 125 } )+(\sqrt [ 2 ]{ 625 } )^{ 3 }\)
26.
Cube of 26 is
27.
By prime factorisation, find the cube roots of 3375
28.
Is 68600 a perfect cube? If not, find the smallest number by which 68600 must be multiplied to get a perfect cube
29.
If the surface area of a cube is 486 cm2. Find its volume
30.
Find the cube of \(\left( 2+\frac { 3 }{ 5 } \right) \).
31.
If the volume of a cube is 729 cm3, then find the length of its side.
32.
Which of the following is a perfect cube?
10,00,00, 225, 343, 270000
1.
(a) 32768
(b) 2744
(f) 21952
2.
(a) 1331
(e) 3375
(f) 4913
3.
Verification
4104 = 4096 + 8 = 163 +23
4104 = 3375 + 729 = 153 + 93
13832 = 5832 + 8000 = 183 + 203
and 13832 = 13824 + 8 = 243 + 23
Hence, it is the required verification.
4.
We have, 2744
Resolving 2744 into prime factors, We get
2744= 2 x 2 x 2 x 7 x 7 x 7 =(2 x 7)3=(14)3
Clearly, prime factor of2744 are grouped into triplets
So,2744 is a perfect cube of 14.
5.
(b)
6.
(b)
7.
(b)
8.
(a)
9.
(b)
10.
11
11.
Given, {52 + (122)1/2}3
Now, (5)2 = 25
(122)1/2=(12) 2 x 1/2 =(12)1 =12
So, (25 + 12)3 =(37)3 = 50653
12.
(a)
6
13.
(c)
7
14.
(d)
1728
15.
16.
9
17.
∵ 7 x 7 x 7 = 343
So, cube of a number ending in 7 will end in the digit 3.
18.
∵ 72 = 2 x 2 x 2 x 3 x 3
So, dividing by 3 x 3 = 9, we get a perfect cube.
19.
∵ 250 = 5 x 5 x 5 x 2 ∴ Least number = 2 x 2 =4
20.
The cube root of a number x is denoted by \(\sqrt [ 3 ]{ x } \) or x1/3.
21.
(1.2)3 = (1.2) x (1.2) x (1.2) = 1.728
22.
( )
10
23.
( )
4
24.
( )
3
25.
( )
15630
26.
( )
17576
27.
15
28.
5
29.
A cube has 6 equal surfaces.
Let side of the cube be x.
\(\therefore\)Area of a surface =x2
\(\Rightarrow\) Area of the given cube = 6x2
\(\therefore\)6x2= 486 \(\Rightarrow x^2={486\over6}=81\)
\(\Rightarrow x =\sqrt{81}=9\)
Thus, the volume of the given cube = 729 cm3 .
30.
\(\frac { 2197 }{ 125 } \)
31.
9 cm
32.
( )
343
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