Question

The ratios of surface areas of 2 cubes are given in List–I. In List–II, the ratios of their volumes are given. Match them :

List-1	List-II
A. 1 ∶ 16	1. 1 ∶ 125
B. 1 ∶ 25	2. 1 ∶ 27
C. 1 ∶ 9	3. 1 ∶ 36
	4. 1 ∶ 64

1. A - 4, B - 1, C - 2
2. A - 3, B - 1, C - 2
3. A - 4, B - 1, C - 3
4. A - 2, B - 4, C - 3

Answer 1

Correct Answer - Option 1 : A - 4, B - 1, C - 2

Given:

List 1 for surface area List 2 for the volume of cubes

List-1	List-II
A. 1 ∶ 16	1. 1 ∶ 125
B. 1 ∶ 25	2. 1 ∶ 27
C. 1 ∶ 9	3. 1 ∶ 36
	4. 1 ∶ 64

 

Concept used:

The ratio of the side of the cube is the square root of the ratio of the surface area.

The ratio of volumes is the cube the ratio of sides of the cube

Calculation:

From list 1

A ratio of surface area 1 : 16 

⇒ the ratio of sides of the cube is 1 : 4 

⇒ the ratio of sides of the cube is 1³ : 4³ = 1 : 64 

⇒ A from List 1 match with 4 of List 2 

B ratio of surface area 1 : 25

⇒ the ratio of sides of the cube is 1 : 5 

⇒ the ratio of sides of the cube is 13 : 53 = 1 : 125

⇒ B from List 1 match with 1 of List 2 

C ratio of surface area 1 : 9 

⇒ the ratio of sides of the cube is 1 : 3 

⇒ the ratio of sides of the cube is 13 : 33 = 1 : 27 

⇒ C from List 1 match with 2 of List 2 

∴ We match the List 1 and List 2 as A - 4, B - 1, C - 2