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

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

### 2 Answers by Expert Tutors

Jim S. | Physics (and math) are fun, reallyPhysics (and math) are fun, really
4.7 4.7 (186 lesson ratings) (186)
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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
Shelly J. | Excellent Maths Tutoring for academic successExcellent Maths Tutoring for academic su...
5.0 5.0 (257 lesson ratings) (257)
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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