Question

Two cubes have volume in the ratio 1:27. FInd the ratio of the area of the face of one to that of the other.

Answer 1

Hey there!!

The formula for the volume of the cube = ( side )³

Let us take the side of the 1st as ' a '

Let us take the side of the 2nd cube as ' b '

Their volumes = a³ and b³

Which means

a³ / b³ = 1 / 27

( a / b )³ = ( 1 / 3 )³

a / b = 1 / 3

Now, the ratio of their sides = 1 :
3

The ratio to their sides =

( a / b )2 = ( 1 / 3 )2

Required answer = 1 / 9

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Answer 2

let side are x and 27x
side of first = cube root x
second = cube root 27x = 3cube root x
ratio = cube root x /3cube root x
1/3 = 1:3