Question

If the edge of a cube is tripled, find the ratio of the surface areas and that of a volume of two cubes.

Answer 1

Old volume[math]=x^3[/math]

New Volume[math]=(3x)^3=27x^3[/math]

Are you asking how many times larger the new volume is? It is [math]27[/math] times bigger than the original, or has [math]2700\%[/math] more volume than the original.

Or, are you asking how much is the difference between the volumes? It is [math]26[/math] times the smaller volume. So this increases the volume by [math]2600\%[/math]

Answer 2

a1 = a , a2 = 3a
so s1/s2 = 6(a1)^2/6(a2)^2
ratio = a2/9a2
= 1:9
so volume ratio = a3/(3a)3
= 1:27