Let the radius of 1st sphere be \’r1\’ and the radius of 2nd sphere be \’r2\’According to question,Ratio\xa0of the volume of the given spheres is,{tex}\\frac { \\text { Volume of } 1 ^ { \\text { st } } \\text { sphere } } { \\text { Volume of } \\Pi ^ { \\text { nd } } \\text { sphere } } = \\frac { \\frac { 4 } { 3 } \\pi r _ { 1 } ^ { 3 } } { \\frac { 4 } { 3 } \\pi r _ { 2 } ^ { 3 } } = \\frac { 8 } { 27 }{/tex}{tex}\\therefore \\quad \\quad \\frac { r _ { 1 } ^ { 3 } } { r _ { 2 } ^ { 3 } } = \\frac { 8 } { 27 }{/tex}{tex} \\frac { r _ { 1 } } { r _ { 2 } } = \\frac { 2\\sqrt2} { 3 }{/tex}The ratio\xa0of the radius of the given spheres, r1\xa0: r2\xa0= 2{tex}\\sqrt 2{/tex}:3Now,Ratio of the\xa0surface areas of the spheres\xa0{tex}= \\frac { \\text { Surface area of } 1 ^ { \\text { st } } \\text { sphere } } { \\text { Surface area of } \\Pi ^ { \\text { nd } } \\text { sphere } }{/tex}{tex}\\frac { 4 \\pi r _ { 1 } ^ { 2 } } { 4 \\pi r _ { 2 } ^ { 2 } } = \\left( \\frac { r _ { 1 } } { r _ { 2 } } \\right) ^ { 2 }{/tex}{tex}=\\left( \\frac { 2\\sqrt2 } { 3 } \\right) ^ { 2 } = \\frac { 8 } { 9 }{/tex}= 16 : 9