# 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.