Question

The ratio between the volumes of two sphere is 8:27.Find the ratio between their areas

Answer 1

heya mate here is your answer

Answer 2

$Ratio\: of \:volumes$

$= 8: 27$

$\frac{v_{1} }{v_{2} } = \frac{8}{27} \\ \\ \frac{ \frac{4}{3}\pi {r _{1} }^{3} }{ \frac{4}{3}\pi {r_{2}}^{3} } = \frac{8}{27} \\ \\ \frac{{r _{1} }^{3}}{{r_{2}}^{3}} = \frac{ {2}^{3} }{ {3}^{3} } \\ \\ \frac{ r_{1}}{ r_{2} } = \frac{2}{3}$

$Surface \: area \: of \: a \: sphere = 4\pi {r}^{2}$

$Ratio \: of \: Areas = \frac{4\pi {r_{1}}^{2} }{4\pi {r_{2}}^{2} } \\ \\ = \frac{{r_{1}}^{2}}{{r_{2}}^{2}} \\ \\ = \frac{ {2}^{2} }{ {3}^{2} } \\ \\ = \frac{4}{9} \\ \\ = 4 : 9$

$Answer \: = 4 : 9$