Question

(Q) If the volumes of two cubes are in the ratio 27:64,then the ratio of their total surface areas is

Answer 1

let the side of first cube be a and other one be b

ratio of their respective volume:

a³:b³

27:64

so a=3

and b=4

now TSA of cube (in ratio)

6a²:6b²

a²:b²

3²:4:

9:16

thank you

Answer 2

volume ratio = 27:64
1st cube =27
side of cube
$a = \sqrt{27} \\ a = 3$
surface area of 1st cube = 6a^2=6×3×3=54

2nd cube = 64
side of 2nd cube
$a = \sqrt{64 } \\ a = 4$
surface area of 2nd cube =6a^2 = 6×4×4=96

ratio of surface area of cubes =54:96 =9:16