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The surface areas of two spheres are in the ratio 1:2 then ratio of their volume is _ |
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Answer» 1:2√2 The answer is 1:2√2 Let be the surface area of 1st sphere and 2nd sphere are 1x and 2x respectively.Then,According to the area of sphere we have,4πr²=1x. ...(i)And,Similarly,4πR²=2x ....(ii)From (i) and (ii) equation,(r/R)²=1/2Hence, R=√2r ....(iii)Now the volume of 1st sphere is 4/3πr³ ....(iv)And,Volume of 2nd sphere is 4/3π(R)³ .....(v)Now put the value of R from (iii) in (v) such that,4/3π(√2r)³=4/3π2√2³= 8√2/3πr³ ....(vi)Now from iv and vi we conclude the ratio of the volumes of given spheres,=1:2√2 |
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