Volume of two spheres are in the ratio of 64:21. Find their radii.
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Radius of one sphere = R
radius of second sphere =r
ratio of volumes = V/v=64/27
(4/3πR³)/(4/3πr³)=4³/3³
R³/r³=4³/3³
R/r = 4/3
R = 4r/3-----(1)
sum of the radii = 21
R+r =21
4r/3 +r =21 [ from (1)]
(4r+3r)/3=21
7r/3=21
r= 21*3/7
r=3*3
r=9
substitute r=9 in (2)
R+r =21
R+9=21
R =21-9
R =12
therefore
R=12, r=9
radius of second sphere =r
ratio of volumes = V/v=64/27
(4/3πR³)/(4/3πr³)=4³/3³
R³/r³=4³/3³
R/r = 4/3
R = 4r/3-----(1)
sum of the radii = 21
R+r =21
4r/3 +r =21 [ from (1)]
(4r+3r)/3=21
7r/3=21
r= 21*3/7
r=3*3
r=9
substitute r=9 in (2)
R+r =21
R+9=21
R =21-9
R =12
therefore
R=12, r=9
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Ratio of given two volumes of sphere is not right .It must be 64:27⬆⬆
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