Q 1 – Which of the following number is not a cube number?
(a) 100000
(b) 3375
(c) 125
(d) 1331
Q 2 – The cube of an even natural number is
(a) odd
(b) even
(c) may be even, may be odd
(d) prime number
Q 3 – If the digit in one place of a number is 6, then its cube will end with its digits
(a) 2
(b) 3
(c) 6
(d) 9
Q 4 – The volume of a cubical box is 343 cm³ which of the following is the side of the box?
(a) 5 cm
(b) 4 cm
(c) 6 cm
(d) 7 cm
Q 5 – The number of zeros at the end of the cube root of the cube number 1000000 is…
(a) 1
(b) 2
(c) 3
(d) 4
Q 6 – Find the smallest number by which the number 72 must be multiplied to obtain a perfect cube.
(a) 2
(b) 3
(c) 4
(d) 8
Q 7 – Fill in the blanks:
a) In the given numbers 6, 12, 24, 48, 64, 100 and 125, the perfect cubes are _______ and __________.
b) The number of zeros at the end of the cube of the number 30 is _________.
c) The volume of the cube is 343 cm³. The edge of the cube is __________.
d) There are________ perfect cubes between 1 and 1000.
e) The cube of an odd number is always an _________ number.
Q 8 – Find the cubes of the following:
(a) 0.3
(b) 0.8
(c) .001
(d) 2 – 0.3
Q 9 – Parikshit makes a cuboid of plastic of sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube?
Q 10 – By what smallest number should 3600 be multiplied so that the quotient is a perfect cube. Also find the cube root of the quotient.
Q 11 – Three numbers are in the ratio 1:2:3 and the sum of their cubes is 4500. Find the numbers.
Q 12 – Write cubes of 5 natural numbers which are of the form 3n+1(e.g. 4,7 10…) and verify the following: ‘The cube of a natural number of the form 3n +1 is a natural number of the same form.
Q 13 – Find the cube root of each of the following numbers by prime factorisation method.
a) 15625
b) 46656
Q 14 – Difference of two perfect cubes is 189. If the cube root of the smaller of the two numbers is 3, find the cube root of the larger number.
Q 15 – Find the smallest number that must be subtracted from 792 to make it a perfect cube. Also, find the cube root of this perfect cube.
Q 17 – The volume of a cubical box is 17.576 m3. Find the length of the side of the box.