There are two cubes. Their lengths are in the ratio 3:4, what is the simplified ratio between their volumes?

Answer 1

a1 = side length of first cube

a2 = side length of second cube

V1 = volume of first cube

V2 = volume of second cube

a1 / a2 = 3 / 4 Multiply both sides by a2

a1 = 3 a2 / 4 = ( 3 / 4 ) a2

V1 / V2 = a1³ / a2³ =

[ ( 3 / 4 ) a2 ]³ / a2³ =

( 27 / 64 ) a2³ / a2³ = 27 / 64