Question

Ratio of two surface area of two cubes is 1:25 find the ratio of their volumes

Answer 1

SInce the surface area of cubes is given by 6$a^{2}$ where   'a' is the length of each side of the cube .
So according to the question let the side length of one cube be 'x ' and side length of other cube be 'y'  
According to  question ratio of surface area is 1:25
⇒6$x^{2}$/6$y^{2}$=1:25
⇒x/y=1/5
Now we have to find ratio of volumes 
 Volume of a cube is  $x^{3}$   where 'x' is the length of the side of cube .
∴  Ratio of volumes both the cubes is $x^{3}$/$y^{3}$=$(1/5)^{3}$
⇒1/125

Answer 2

Solution:-

Let the edges of the two respective cubes be 'x' and 'y'

Then,
x²/y² = 1/4
Or, (x/y)² = (1/2)²
Or, (x/y) = 1/2

Ratio of their respective volumes = 6x³/6y³ = x³/y³
⇒ (x/y)³ = (1/2)³
⇒ = 1/8
Or, 1:8
So the ratio of their volumes is 1 : 8
Answer.