SOLUTION: The volume of a sphere varies directly as the cube of its radius. If the ratio of the radius of two spheres is 5:3, what is the ratio of the volumes of the spheres? (hint: (r1)/ (r

Algebra ->  Probability-and-statistics -> SOLUTION: The volume of a sphere varies directly as the cube of its radius. If the ratio of the radius of two spheres is 5:3, what is the ratio of the volumes of the spheres? (hint: (r1)/ (r      Log On


   

Question 1105282: The volume of a sphere varies directly as the cube of its radius. If the ratio of the radius of two spheres is 5:3, what is the ratio of the volumes of the spheres? (hint: (r1)/ (r2)=5/3)
Found 2 solutions by Fombitz, greenestamps:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
V%5B1%5D=%284%2F3%29pi%2AR%5B1%5D%5E3
.
.
V%5B2%5D=%284%2F3%29pi%2AR%5B2%5D%5E3
.
.
R%5B1%5D%2FR%5B2%5D=5%2F3
R%5B2%5D=%283%2F5%29R%5B1%5D
So,
V%5B2%5D=%284%2F3%29pi%2A%28%283%2F5%29R%5B1%5D%29%5E3
V%5B2%5D=%2827%2F125%29%2A%284%2F3%29pi%2AR%5B1%5D%5E3
and,

highlight%28V%5B2%5D%2FV%5B1%5D=27%2F125%29

Answer by greenestamps(13206) About Me  (Show Source):
You can put this solution on YOUR website!


All spheres are similar. For any similar figures, if the ratio of linear measurements (scale factor) is a:b, then the ratio of area measurements is a^2:b^2 and the ratio of volume measurements is a^3:b^3.

The radius of a sphere is a linear measurement; if the ratio of the radii of two spheres is 5:3, then the ratio of the volumes is 5^3:3^3 = 125:27.