Correct Answer - Option 2 : 49 : 36
Given:
Ratio of volume of two cubes is 2744 : 1728
Formula Used:
Volume of a cube is a3
Total surface area of a cube is 6a2, where a is the side of the cube
Calculation:
Let the side of cubes be a and b
⇒ a3 : b3 = 2744 : 1728
⇒ a3/b3 = 2744/1728
Taking cube root on both sides,
⇒ a/b = 14/12
⇒ a/b = 7/6
Let the sides of a cube be 7x and 6x
Total Surface Area of Cube with side 7x = 6 × (7x)2
Total Surface Area of Cube with side 6x = 6 × (6x)2
Ratio of Total surface area of cubes,
⇒ 6 × (7x)2 ∶ 6 × (6x)2
⇒ 49 ∶ 36
∴ Ratio of Total Surface Area of given cubes is 49 ∶ 36.
