Free Cubes and Cube Roots 02 Practice Test - 8th Grade
Question 1
Amrit's teacher told him "Go to shop A and buy 3 chocolates. Then go to shop B and buy thrice the number of chocolates you have and eat 3 chocolates. Then go to shop C and again buy thrice the number of chocolates you have." What will be the number of chocolates left with Amrit at the end?
27
48
45
SOLUTION
Solution : B
Number of chocolates Amrit has after going to shop A = 3
Number of chocolates Amrit has after going to shop B = 3 x 3 + 3 = 12
Number of chocolates Amrit has after shop B and eating 3 = 12 - 3 = 9
Number of chocolates Amrit has after going to shop C = 3 x 9 + 9 = 36
Hence, the number of chocolates Amrit has at the end is 36.
Question 2
The digit in the units place in the cube of 298 is
2
3
8
4
SOLUTION
Solution : A
The digit in the units place in 298 is 8.
cube of 8 is 512, which ends in 2.
Hence, the digit in the units place in the cube of 298 is 2
Question 3
Find the cube root of 216 × 729.
54
9
6
51
SOLUTION
Solution : A
216 is the cube of 6 as 216 can be expressed as (6×6×6)
729 is the cube of 9 as 729 can be expressed as (9×9×9)
3√6×6×6×3√9×9×9
= 6×9
So the cube root of the product will be 6 × 9 = 54.
Question 4
Find the number whose square is the sum of the cube of the first 5 natural numbers.
10
12
13
15
SOLUTION
Solution : D
The sum of first 5 natural numbers can be expressed as (n(n+1)2)2 where n = 5, which gives us
((5×6)2)2 =(302)2 = 152
Thus the cubes of first 5 natural numbers can be expressed as the square of 15.
Question 5
How many cubes of side length 3 can be fit in a cuboid of dimension 3×6×9?
2
6
9
10
SOLUTION
Solution : B
Volume of cuboid = 3×6×9 =162 cubic units
Volume of cube = 3×3×3= 27 cubic units
Number of cubes that can be fit in the cuboid is 16227 = 6
Question 6
How many perfect cubes are there between 0 and 100?
SOLUTION
Solution : C
Cube of 1 = 1
Cube of 2 = 8
Cube of 3 = 27
Cube of 4 = 64
So total 4 numbers have their cubes that lie between 0 and 100
Question 7
The cube root of 30 lies between 5 and 6.
False
SOLUTION
Solution : B
The cube of 3 = 27
The cube of 4 = 64
Since 30 lies between 27 & 64 so its cube root must lie between 3 & 4.
Hence, the given statement is false.
Question 8
What is the value of 3√8 + 13√8 ?
2
2.5
0.5
1
SOLUTION
Solution : B
8= 2 x 2 x 2
Cube root of 8 = 2
So 2+ 12 = 2.5
Question 9
The cube of 0 is
SOLUTION
Solution :Cube of 0 is 0 (anything multiplied to 0 is 0)
Question 10
When the cube root of 8 is multiplied with the cube root of -8, the result which cannot be obtained is
8
-8
4
SOLUTION
Solution : A, B, and C
Cube root of 8 is 2 and cube root of -8 is -2. When they are multiplied together, the result is -4.