The ratio of the volumes of two spheres is 8 is to 27 what is the ratio of their surface areas

The ratio of the volumes of two spheres is 8 is to 27 what is the rati

1.	The ratio of the volumes of two spheres is 8 is to 27 what is the ratio of their surface areas
Answer» 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