# Free Cubes and Cube Roots 03 Practice Test - 8th Grade

What is the units digit of the cube of the number whose unit digit is 7?

A.

3

B.

5

C.

4

D.

2

#### SOLUTION

Solution : A

The units digit of the cube of 7 i.e.343 is 3.
Thus, the units digit of the cube of the number whose unit digit is 7 will be 3.

What is the value of  383216 ?

A.

4

B.

-8

C.

-4

D.

8

#### SOLUTION

Solution : A

-  8  = - 2×2×2

38 = 2

-  216  = 6×6×6

3216 = 6

So the given expression 383216 becomes - 2 - (- 6) = - 2 + 6

= 4

What should be multiplied to 43200 to make it a perfect cube?

A.

2

B.

3

C.

5

D.

Already a perfect cube

#### SOLUTION

Solution : C

For a number to be a perfect cube, its prime factors should be in the form of triplets
By prime factorization, 43200 =  26× 33× 52

Only two 5’s are there so we need one more 5 to make a triplet.

So if 43200 is multiplied by 5, we get a perfect cube.

Which of the following could be the cube of 37?

A.

50653

B.

50666

C.

50892

D.

55018

#### SOLUTION

Solution : A

The cube of an odd number is odd. So only 50653 is possible. We can also check the answer by calculating the cube of 37
= 37 × 37  × 37  = 50653.

Which of these is not a perfect cube?

A.

343

B.

1331

C.

512

D.

81

#### SOLUTION

Solution : D

By prime factorization, we have

343=7×7×71331=11×11×11  512=8×8×8    81=3×3×3×3

For a number to be a perfect cube ,each of its factors must be repeated thrice.
343, 1331 and 512 are the perfect cubes of 7, 11 and 8 respectively, whereas 81 is not, as 3 is repeating 4 times which is not a triplet.

81 is not a perfect cube.

With what number should 1715 be divided to get a perfect cube?

A.

1

B.

7

C.

5

D.

Already a perfect cube

#### SOLUTION

Solution : C

For a number to be a perfect cube, its prime factors should be expressed as triplets
By prime factorization, we get 1715 = 7×7×7×5

We have three 7’s but only one 5 so we need to divide the number by 5.

100 is the smallest square number that is the sum of cubes of 4 consecutive natural numbers.

A.

True

B.

False

#### SOLUTION

Solution : A

100 = 102
= 13+ 23+ 33+ 43
= 1+8+27+64

Anshul and Balendu have 50 cubes of side 1 cm. They decided to make a larger cube by joining these smaller cubes. The number of larger cubes (all of different sizes) they can make is

___

#### SOLUTION

Solution : Since the side of the smaller cube is 1 cm, its volume will be 1 cubic cm.

We know that the volume of cubes of sides 1,2,3,4,... are 1,8,27,64...cubic cm.
But Anshul and Balendu have only 50 small cubes, so they can make cubes of 3 sizes with the help of 1,8 and 27 smaller cubes.
It should be noted that (50-1-8-27) = 14 smaller cubes will be left unused.

The cube of a number is less than its square in which of the following cases ?

A.

The number lies between -1 and 0

B.

The number is 0

C. The number lies between 0 and 1
D. The number lies between 1 and 2

#### SOLUTION

Solution : A and C

Cube of a negative number is negative but square of a negative number is positive. Thus, for a number lying between -1 and 0, the cube is less than its square.
The cube as well as the square of 0 is zero. For decimal numbers less than 1, the cube of a number is lesser than its square. For a number greater than 1, its cube is greater than its square.

The cube of average of 3 and 7 will also be the average of the of the cubes of 3 and 7.

A.

True

B.

False

#### SOLUTION

Solution : B

The average of 3 and 7 is 5. The cube of 5 is 125. The cube of 3 and 7 is 27 and 343 respectively. The average of 27 and 343 is 185 which is not the cube of 5.