The ones digit of the cube of 23 is
- A3
- B6
- ✓7
- D9
Answer: C.
View full solution →Question types
Cubes and Cube Roots question types
97 questions across 11 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
97
Questions
11
Question groups
5
Question types
01
M.C.Q. [1 Marks Each]
10 Q→02TRUE-FLASE [1 Marks Each]
12 Q→03Assertion (A) & Reason (B) MCQ
3 Q→042 Marks Questions
7 Q→053 Marks Question
16 Q→065 Marks Questions
7 Q→07Case study (4 Marks)
1 Q→08MATCH THE FOLLOWING.
1 Q→091 Marks Question
30 Q→10BLANKS [1 Marks Each]
5 Q→114 Mark Question
5 Q→Sample Questions
Cubes and Cube Roots questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Which of the following numbers is not a perfect cube?
- A216
- B343
- C125
- ✓667
Answer: D.
View full solution →What is the value of $\frac{\sqrt[3]{64}+\sqrt[3]{125}}{\sqrt[3]{27}} ?$
- A2
- ✓3
- C4
- D9
Answer: B.
View full solution →The cube of a number is divided by the number itself. The result is 36. What is the number?
- A4
- ✓6
- C36
- D216
Answer: B.
View full solution →The value of $\sqrt[3]{512} \times \sqrt[3]{27}$ is
- ✓24
- B$-24$
- C48
- D$-48$
Answer: A.
View full solution →The cube of a single digit number may be a single digit number.
The cube of a two-digit number may have seven or more digits.
The cube of a two digits number may be a three digits number.
There is no perfect cube which ends with 8.
If square of a number ends with 5, then its cube ends with 25.
Assertion (A) The ones digit in the cube root of the cube number 100000 is 0.
Reason (R) The cube root of a number is the factor that we multiply by itself three times to get that number.
Reason (R) The cube root of a number is the factor that we multiply by itself three times to get that number.
- ABoth A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- ✓A is false but R is true.
Answer: D.
View full solution →Assertion (A) Finding the cube root of a number is the inverse operation of finding the cube of that number.
Reason (R) If you take the cube root of a number and then cube, the result you will get back to the original number.
Reason (R) If you take the cube root of a number and then cube, the result you will get back to the original number.
- ✓Both A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
Answer: A.
View full solution →Assertion (A) The cube of an even number is always an even number.
Reason (R) When you multiply an even number by itself three times, the result is always even.
Reason (R) When you multiply an even number by itself three times, the result is always even.
- ✓Both A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
Answer: A.
View full solution →Express the following numbers as the sum of odd numbers using the pattern given below
(i) $6^3$$\quad$(ii) $8^3$$\quad$(iii) $7^3$
$\begin{array}{r}1=1=1^3 \\ 3+5=8=2^3 \\ 7+9+11=27=3^3 \\ 13+15+17+19=64=4^3 \\ 21+23+25+27+29=125=5^3\end{array}$
View full solution →(i) $6^3$$\quad$(ii) $8^3$$\quad$(iii) $7^3$
$\begin{array}{r}1=1=1^3 \\ 3+5=8=2^3 \\ 7+9+11=27=3^3 \\ 13+15+17+19=64=4^3 \\ 21+23+25+27+29=125=5^3\end{array}$
Find the cube root of each of the following number by prime factorisation method:
10648
10648
Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm and 5 cm. How many such cubolds will he need to form a cube?
Find the smallest number by which each of the following number must be divided to obtain a perfect cube :
81
81
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.
Consider the following pattern
$\begin{array}{l}2^3-1^3=1+2 \times 1 \times 3,3^3-2^3=1+3 \times 2 \times 3 \\4^3-3^3=1+4 \times 3 \times 3\end{array}$
Using the above pattern, find the value of the following:
(i) $7^3-6^3$$\qquad\quad$(ii) $12^3-11^3$
(iii) $20^3-19^3$$\quad~~$(iv) $51^3-50^3$
View full solution →$\begin{array}{l}2^3-1^3=1+2 \times 1 \times 3,3^3-2^3=1+3 \times 2 \times 3 \\4^3-3^3=1+4 \times 3 \times 3\end{array}$
Using the above pattern, find the value of the following:
(i) $7^3-6^3$$\qquad\quad$(ii) $12^3-11^3$
(iii) $20^3-19^3$$\quad~~$(iv) $51^3-50^3$
Check which of the following are perfect cubes :
2700
2700
Find the cube root of each of the following number by prime factorisation method:
512
512
Find the cube root of each of the following number by prime factorisation method:
64
64
Find the smallest number by which each of the following number must be divided to obtain a perfect cube :
128
128
Find the length of each side of a cube, if its volume is $512 \text{ cm}^3.$
View full solution →Evaluate $\left(5^2+\left(12^2\right)^{1 / 2}\right)^3.$
View full solution →Difference of two numbers which are perfect cubes is 189. If the cube root of the smaller of the two numbers is 3, then find the cube root of the larger number.
To collect rain water, Aditya made a cubical tank which can hold $91125\text{ m}^3$ water. He uses this water for watering the plants of his garden.
(i) What is the height of the tank?
(ii) What value is depicted here?
View full solution →(i) What is the height of the tank?
(ii) What value is depicted here?
Evaluate $\sqrt[3]{27}+\sqrt[3]{8}+\sqrt[3]{64}$
View full solution →Interlocking cubes come in different colours. Different shapes can be created by joining them.
Sasha is making large cube using small interlocking cubes. She starts with a yellow cube and then fits one layer of red cubes around it to make the large cube.
On the basis of above given information, answer the following questions.
(i) What is the number of red cubes used?
(a) 9 $~~\quad$ (b) 18
(c) 26 $\quad$ (d) 27
(ii) Sasha considers the red layer as the first layer on the yellow cube. Which equation can be used to find the number of red cubes?
(a) $6 x^2$ $~\qquad$ (b) $x^3$
(c) $x^3+1$ $\quad$ (d) $2(x+2)^2+4 x^2$
(iii) The red cube is surrounded by a layer of green cubes. The resulting figure is also a cube. What is the number of green cubes used?
(iv) Shubham puts $\text x$ layers around the yellow cube. How many small cubes did he use on the top-most face of the large cube so formed?
View full solution →Sasha is making large cube using small interlocking cubes. She starts with a yellow cube and then fits one layer of red cubes around it to make the large cube.
On the basis of above given information, answer the following questions.
(i) What is the number of red cubes used?
(a) 9 $~~\quad$ (b) 18
(c) 26 $\quad$ (d) 27
(ii) Sasha considers the red layer as the first layer on the yellow cube. Which equation can be used to find the number of red cubes?
(a) $6 x^2$ $~\qquad$ (b) $x^3$
(c) $x^3+1$ $\quad$ (d) $2(x+2)^2+4 x^2$
(iii) The red cube is surrounded by a layer of green cubes. The resulting figure is also a cube. What is the number of green cubes used?
(iv) Shubham puts $\text x$ layers around the yellow cube. How many small cubes did he use on the top-most face of the large cube so formed?
Match the Column A to Column B
View full solution →| Column A | Column B |
| (i) Cube of 26 is | (a) 17576 |
| (ii) Cube root of 21952 | (b) 144 |
| (iii) $\sqrt[3]{125}+(\sqrt[2]{625})^{3}$ | (c) 28 |
| (iv) $(\sqrt[2]{25})^3+\sqrt[3]{6859}$ | (d) 15630 |
Find the ones digit of the cube of each of the following number :
53
53
Find the ones digit of the cube of each of the following number :
5022
5022
Find the ones digit of the cube of each of the following number :
77
77
Find the ones digit of the cube of each of the following number :
1024
1024
Find the ones digit of the cube of each of the following number :
1005
1005
The least number by which 72 is divided to make it a perfect cube is _____________.
Cube of a number ending in 7 will end in the digit _____________.
Ones digit in the cube of 27 is _____________.
There are _____________ perfect cubes between 1 and 1000.
The cube of 90 will have _____________ zeroes.
Which of the following are perfect cubes?
(i) 400 $\qquad~~$ (ii) 3375 $\quad$ (iii) 8000
(iv) 15625 $\quad$ (v) 9000 $\quad$ (vi) 6859
(vii) 2025 $\quad~$ (viii) 10648
View full solution →(i) 400 $\qquad~~$ (ii) 3375 $\quad$ (iii) 8000
(iv) 15625 $\quad$ (v) 9000 $\quad$ (vi) 6859
(vii) 2025 $\quad~$ (viii) 10648
Check which of the following are perfect cubes :
16000
16000
Find the smallest number by which each of the following number must be multiplied to obtain a perfect cube :
256
256
Find the smallest number by which each of the following number must be multiplied to obtain a perfect cube :
243
243
Which of the following numbers are not perfect cubes?
(i) 216$\qquad$(ii) 128$\quad$(iii) 1000
(iv) 100$\quad~~$(v) 46656
View full solution →(i) 216$\qquad$(ii) 128$\quad$(iii) 1000
(iv) 100$\quad~~$(v) 46656
Generate a Cubes and Cube Roots paper free
Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.