V=4/3πr3 and solve for r.?

Question

How do I solve the equation ( V = \frac{4}{3} \pi r^3 ) for ( r )? I'm interested in understanding the steps involved in isolating ( r ) in this volume formula for a sphere.

Anonymous · Accepted Answer

V=4/3&pi; r^3r^3 = 3/4*V/&pi;r= Qubic root of [3/4 * V/&pi;].P.S. I don't understand your answer; 6pi2V over 2pi would be the same as 6V and that isn't right. It could be right if you had some extra information about r in the terms of V or something similar. I just don't know.Sorry!

Anonymous · Answer

V = 4/3 TT r^3 , taking TT for Pi since I couldn't write it

Divide both side by 4/3: 'Anything' divided by a number of the form a/b where b is different from 0, is the same as 'Anything' multiplied by b/a, wherever a is different from 0. So then V divided by 4/3 = 3/4 V.... right? And similar division of the equation on the right gets rid of the 4/3.

3/4 V = TT r^3 ... now divide both sides by pi and you will have

3/41/TTV = 3V/4TT = r^3.... then take the cube root of both sides. The one on the right becomes r. Therefore,

r = (3V/4TT)^1/3 .... Remember when a number is raised to any number 1/a (where a is different from 0), it is the same as computing the ath root of that number. So raising 3V/4TT to 1/3 means the cube root of 3V/4TT. So your answer is:

r = (3V/4TT)^1/3

Tito Heidenreich · Answer

Volume of a sphere= 4/3piradius^3
To solve for "r" you need to know the volume
To find the volume you need to know what r is.

Anonymous

V=4/3πr3 and solve for r.?

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