if a man wants to calculate the WEIGHT of a perfect ball of metal, he would use Volume=(4π*R*R*R)/3 then multiply the answer times the density of a given material. The question is, how would you write the formula to reverse this process.
All you know is the overall weight of the ball. Tell me how many inches a 10 pound ball is. (Density of metal is 0.409lbs per cube inch)

Question

if a man wants to calculate the WEIGHT of a perfect ball of metal, he would use Volume=(4π*R*R*R)/3 then multiply the answer times the density of a given material.  The question is, how would you write the formula to reverse this process.
All you know is the overall weight of the ball. Tell  me how many inches a 10 pound ball is.  (Density of metal is 0.409lbs per cube inch)

cwrw238 · Answer

w = (4/3)* pi* r^3 * d

anonymous · Answer

WOW that was fast, than you@   Its been driving me nuts lol

cwrw238 · Answer

what do u mean by how many inches? do you mean the radius r?

anonymous · Answer

Yes The problem is in there too,  0.409 lbs per square inch, and its a 10 pound ball...  so I got to structure this to where I can tell what radius or diameter the ball is.

anonymous · Answer

excuse me,  0.409 lbs per CUBIC inch lol

cwrw238 · Answer

rearranging the formula

r^3 = w / ( 4/3 * pi * d)

klimenkov · Answer

$$\text{weight}=\text{volume}\times \text{density}$$$$\text{volume}=\frac {\text{weight}} {\text{density}}$$$$\text{volume}=\frac {4} {3} \pi R^3$$

anonymous · Answer

Me thinks too that the metal is lead, the specific gravity is about that of lead from what I can tell now,  its bonus points lol  I got  that figured out,

cwrw238 · Answer

r^3 = 10 / (4/3 * 3.14 * 0.409)

r is cube root of this

anonymous · Answer

ok thank you,  that looks right what I needed there