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.
Answer & explanation
Correct answer: option 1
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 = \(\frac{3^2}{4^2}\) = \(\frac{9}{16}\)