The ratio between the volume of two spheres is 8 : 27. What is the ratio between their surface areas?

Question

KollegeApply · Accepted Answer

4 : 9 Let the radii of the spheres be R and r, respectively. Then, ratio of their volumes = ($\frac{4}{3}$pi"R"^3)/($\frac{4}{3}$pi"r"^3) Therefore, `($\frac{4}{3}$pi"R"^3)/($\frac{4}{3}$pi"r"^3) = $\frac{8}{27}$ => R^3/"r"^3 = $\frac{8}{27}$ => ("R"/"r")^3 = ($\frac{2}{3}$)^3 => R/r = $\frac{2}{3}$` Hence, the ratio between their surfcae areas =(4pi"R"^2)/(4pi"r"^2) = "R"^2/"r"^2 =($\frac{2}{3}$)^2 = $\frac{4}{9}$ = 4 : 9

AChoose Your Answer