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If the ratio of curved surface areas of two solid spheres is 16:9, the ratio of their volumes isA. `64:27`B. `4:3`C. `27:64`D. `3:4` |
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Answer» Let the radii of two solid spheres be `r_(1)` units and `r_(2)` units respectively. `therefore` the curved surface areas of the spheres are `4pi_(1)^(2)" ""sq-units and"" "4pi_(2)^(2) `sq-units respectively As per question, `4pir_(1)^(2):4pir_(2)^(2)=16:9rArr(4pir_(1)^(2))/(4pir_(1)^(2))=(16)/(9)rArr(r_(1)/(r))^(2)=((4)/3)^(2)rArrr_(1)/r_(2)=(4)/(3)` `therefore` The ratio of their volumes =`=(4)/(3)pir_(1)^(3):=(4)/(3)pir_(2)^(3)=(4/3pir_(1)^(3))/(4/3pir_(2)^(3))=(r_(1)/(r_(2)))^(3)=((4)/(3))^(3)=(64)/(27)=64:27` `therefore` is correct. |
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