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The ratio of the volumes of two spheres is 64:125. What is the ratio of their radii?

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2 Answers

Omar,
           All you need to solve this problem is V = c* r3 where c=(4/3)π and is a constant. If we now apply this relationship to the problem we have 64/125=(r1/r2) solving for the ratio of the radii gives
 
           (r1/r2)=(64/125)1/3 =.8 or 4/5
 
Hope this helps
 
Jim
Hi Omar,
 
Volume of the sphere=(4/3)Πr³
 
Let V1 be the volume of first sphere with radius r
 
and Vbe the volume of second sphere with radius R
 
The ratio of the volumes of two spheres is 64:125.
 
V1/V2= (4/3)∏r³/(4/3)ΠR³=64/125

Cancelling (4/3)Π, we get
 
r³/R³=64/125=4³/5³
 
(r/R)³=(4/5)³
 
r/R=4/5
 
The ratio of their radii=4/5=4:5

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