the ratio of volume of two spheres is 27:8. find the ratio of there surface area
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![formula \: of \:volume \: of spheres \: = \frac{4}{3}\pi {r}^{3} \\ \\ here \: given \: the \: ratio \: of \: volume \: of \: spheres \: = 27\ratio8 \\ \\ \frac{ \frac{4}{3}\pi {r1}^{3}}{ \frac{4}{3}\pi {r2}^{3} } = \frac{27}{8} \\ \\ \frac{ {r1}^{3} }{ {r2}^{3} } = \frac{27}{8} \\ \\ \frac{r1}{r2} = \frac{ \sqrt[3]{27} }{ \sqrt[3]{8} } = \frac{3}{2} \\ \\ now \: we \: find \: to \: ratio \: of \: area \: of \: spheres \: = \frac{4\pi {r1}^{2} }{4\pi {r2}^{2} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{ {r1}^{2} }{ {r2}^{2} } = {( \frac{r1}{r2} )}^{2} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {( \frac{3}{2} )}^{2} = \frac{9}{4} \\ \\ \\ \\ hope \: it \: helps \: you](https://tex.z-dn.net/?f=formula+%5C%3A+of+%5C%3Avolume+%5C%3A+of+spheres+%5C%3A++%3D++%5Cfrac%7B4%7D%7B3%7D%5Cpi+%7Br%7D%5E%7B3%7D++%5C%5C++%5C%5C+here+%5C%3A+given+%5C%3A+the+%5C%3A+ratio+%5C%3A+of+%5C%3A+volume+%5C%3A+of+%5C%3A+spheres+%5C%3A++%3D+27%5Cratio8+%5C%5C++%5C%5C++%5Cfrac%7B+%5Cfrac%7B4%7D%7B3%7D%5Cpi+%7Br1%7D%5E%7B3%7D%7D%7B+%5Cfrac%7B4%7D%7B3%7D%5Cpi+%7Br2%7D%5E%7B3%7D++%7D++%3D++%5Cfrac%7B27%7D%7B8%7D++%5C%5C++%5C%5C++%5Cfrac%7B+%7Br1%7D%5E%7B3%7D+%7D%7B+%7Br2%7D%5E%7B3%7D+%7D++%3D++%5Cfrac%7B27%7D%7B8%7D++%5C%5C++%5C%5C++%5Cfrac%7Br1%7D%7Br2%7D++%3D++%5Cfrac%7B+%5Csqrt%5B3%5D%7B27%7D+%7D%7B+%5Csqrt%5B3%5D%7B8%7D+%7D++%3D++%5Cfrac%7B3%7D%7B2%7D++%5C%5C++%5C%5C+now+%5C%3A+we+%5C%3A+find+%5C%3A+to+%5C%3A+ratio+%5C%3A+of+%5C%3A+area+%5C%3A+of+%5C%3A+spheres+%5C%3A++%3D++%5Cfrac%7B4%5Cpi+%7Br1%7D%5E%7B2%7D+%7D%7B4%5Cpi+%7Br2%7D%5E%7B2%7D+%7D++%5C%5C++%5C%5C++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%3D++%5Cfrac%7B+%7Br1%7D%5E%7B2%7D+%7D%7B+%7Br2%7D%5E%7B2%7D+%7D++%3D++%7B%28+%5Cfrac%7Br1%7D%7Br2%7D+%29%7D%5E%7B2%7D++%5C%5C++%5C%5C++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A++%5C%3A+++%3D++%7B%28+%5Cfrac%7B3%7D%7B2%7D+%29%7D%5E%7B2%7D++%3D++%5Cfrac%7B9%7D%7B4%7D++%5C%5C++%5C%5C++%5C%5C++%5C%5C+hope+%5C%3A+it+%5C%3A+helps+%5C%3A+you "formula \: of \:volume \: of spheres \: = \frac{4}{3}\pi {r}^{3} \\ \\ here \: given \: the \: ratio \: of \: volume \: of \: spheres \: = 27\ratio8 \\ \\ \frac{ \frac{4}{3}\pi {r1}^{3}}{ \frac{4}{3}\pi {r2}^{3} } = \frac{27}{8} \\ \\ \frac{ {r1}^{3} }{ {r2}^{3} } = \frac{27}{8} \\ \\ \frac{r1}{r2} = \frac{ \sqrt[3]{27} }{ \sqrt[3]{8} } = \frac{3}{2} \\ \\ now \: we \: find \: to \: ratio \: of \: area \: of \: spheres \: = \frac{4\pi {r1}^{2} }{4\pi {r2}^{2} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{ {r1}^{2} }{ {r2}^{2} } = {( \frac{r1}{r2} )}^{2} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {( \frac{3}{2} )}^{2} = \frac{9}{4} \\ \\ \\ \\ hope \: it \: helps \: you")
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