Cubes and Cube Roots Test

Result

Cubes and Cube Roots Test - 2

Score
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Weekly Quiz Competition

Question 1
1 / -0

What is the smallest number by which 3087 must be divided so that the quotient obtained is a perfect cube?

A
6

B
9

C
11

D
12

Solution

3087 = 7 × 7 × 7 × 9
To obtain a perfect cube, we need to divide 3087 by 9.
So, the correct answer is 9.
Question 2
1 / -0

How many cubes of side 3 cm each can be packed in a cubical box with inner side of 6 cm?

A
10

B
6

C
8

D
12

Solution

Side of the smaller cube = 3 cm
Volume of the smaller cube = 3 × 3 × 3 = 27 cm³
Side of the bigger cube (box) = 6 cm
Volume of the bigger cube (box) = 6 × 6 × 6 = 216 cm³
Number of smaller cubes which can be packed in the bigger cubical box = 216/27 = 8
Question 3
1 / -0

What is the smallest number by which 8712 must be divided, so that the quotient obtained is a perfect cube?

A
33

B
11

C
1089

D
2424

Solution

8712 = 2 × 2 × 2 × 3 × 3 × 11 × 11
3 and 11 are not grouped as triplets.
So, the smallest number is 3 × 3 × 11 × 11 = 1089.
Question 4
1 / -0

What is the smallest number by which (2 ×3 ×6)³ × (2 ×3)² must be divided, so that the quotient is a perfect cube?

A
2 × 3

B
(2 ×3)²

C
(3 ×3)²

D
(2 × 2)

Solution

In (2 ×3 ×6)³ × (2 ×3)², (2 ×3)²is not grouped as triplets. So, we divide the number by (2 ×3)².