# Free Cubes and Cube Roots 02 Practice Test - 8th Grade

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?

A.

27

B. 36
C.

48

D.

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.

The digit in the units place in the cube of 298 is

A.

2

B.

3

C.

8

D.

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

Find the cube root of 216 × 729.

A.

54

B.

9

C.

6

D.

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)

36×6×6×39×9×9

= 6×9

So the cube root of the product will be 6 × 9 = 54.

Find the number whose square is the sum of the cube of the first 5 natural numbers.

A.

10

B.

12

C.

13

D.

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.

How many cubes of side length 3 can be fit in a cuboid of dimension 3×6×9?

A.

2

B.

6

C.

9

D.

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

How many perfect cubes are there between 0 and 100?

A. 2
B. 3
C. 4
D. 5

#### 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

The cube root of 30 lies between 5 and 6.

A. True
B.

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.

What is the value of  38138 ?

A.

2

B.

2.5

C.

0.5

D.

1

#### SOLUTION

Solution : B

8= 2 x 2 x 2

Cube root of 8 = 2

So 2+  12 = 2.5

The cube of 0 is

___

#### SOLUTION

Solution :

Cube of 0 is 0 (anything multiplied to 0 is 0)

When the cube root of 8 is multiplied with the cube root of -8, the result which cannot be obtained is

A.

8

B.

-8

C.

4

D. -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.