Question

The ratio of the surface areas of two cubes is 16:36,then their ratio of their sides will be?​

Answer 1

6a²/6b²=16/25;

a²/b²=16/25;

a/b=√16/25;

a/b=4/5 . ratio of volume of cubes:

a³/b³=(a/b)³=(4/5)³=64/125

Answer 2

The ratio of their sides will be 2 : 3

Step-by-step explanation:

Let the side length of the small cube is a and that of the large cube is A.

So, the total surface area of the small cube is 6a² and that of the large cube is 6A².

Now, given that 6a² : 6A² = 16 : 36

⇒ $\frac{a^{2} }{A^{2} }  = \frac{4^{2} }{6^{2} }$

⇒ $\frac{a}{A} = \frac{4}{6}$

⇒ a : A = 4 : 6 = 2 : 3

Therefore, the ratio of their sides will be 2 : 3 (Answer)