Question

2 cubes have a volume in the ratio 1:64. find the ratio of the surface area of the face of one to that of the other.​

Answer 1

Answer:

$\frac{1}{16}$

Step-by-step explanation:

Let the sides of  1st cue be a and 2nd cube be b. Then

Volume of cube 1 / Volume of cube 2 = 1/64

$a^{3}$ /  $b^{3}$ = 1/64

Taking cube root of both sides.

a/b = 1/4

==> b=4a                .............................(i)

S.a of cube 1= 6$a^{2}$

S.a of cube 2= 6$b^{2}$  

===>>> S.a of cube 1 / S.a of cube 1

= $\frac{6a^{2}}{6b^2}$

=$\frac{a^{2}}{b^2}$

=$\frac{a^{2}}{16a^2}$

= $\frac{1}{16}$

Hope it Helps