The ratio between the volumes of Sphere 1 and Sphere 2 is 27 : 64. Find the ratio of the surface areas of Sphere 1 and Sphere 2.

9 : 16

The ratio between the volumes of Sphere 1 and Sphere 2 =  27 ∶ 64.

According to the question,

\(\frac{r^3}{R^3}\) = \(\frac{27}{64}\)  

\(\frac{r}{R}\) = \(\frac{3}{4}\) 

Now the ratio of the surface areas of Sphere 1 and Sphere 2 = \(\frac{3^2}{4^2}\) = \(\frac{9}{16}\)