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| 1. |
The volume of two spheres are in the ratio 64:27. The ratio of there surface area is |
| Answer» Suppose {tex}r_1\\\xa0and\\ r_2{/tex} be the radii of two spheres.{tex}\\therefore{/tex} the ratio of their volumes =\xa0{tex}\\frac{\\frac{4}{3} \\pi r_{1}^{3}}{\\frac{4}{3} \\pi r_{2}^{3}}=\\frac{64}{27}{/tex}\xa0{tex}\\left(\\frac{r_{1}}{r_{2}}\\right)^{3}=\\left(\\frac{4}{3}\\right)^{3}{/tex}\xa0{tex}\\Rightarrow{/tex}\xa0{tex}\\frac{r_{1}}{r_{2}}{/tex}\xa0=\xa0{tex}\\frac{4}{3}{/tex}Ratios of surface areas of two spheres =\xa0{tex}\\frac{4 \\pi r_{1}^{2}}{4 \\pi r_{2}^{2}}{/tex}\xa0{tex}=\\left(\\frac{r_{1}}{r_{2}}\\right)^{2}{/tex}\xa0= ({tex}\\frac{4}{3}{/tex})2 =\xa0{tex}\\frac{16}{9}{/tex}{tex}\\therefore{/tex}Required ratio {tex}= 16: 9.{/tex} | |