SOLUTION: Solve for r: v=1/3(pi)h^2(3r-h) I solved it to get (h+v)/(3pi h^2)=r The solution book says it should be: (3v+pi h^3)/(3pi h^2) What did I do wrong? Or is the book wrong

Question 365565: Solve for r:
v=1/3(pi)h^2(3r-h)
I solved it to get (h+v)/(3pi h^2)=r
The solution book says it should be:
(3v+pi h^3)/(3pi h^2)
What did I do wrong? Or is the book wrong?
Found 2 solutions by Alan3354, unlockmath:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Solve for r:
v=1/3(pi)h^2(3r-h)
3r-h = 3v/(pi*h^2)
3r = h + 3v/(pi*h^2)
3r = (3v + pi*h^3)/(pi*h^2)
r = (3v + pi*h^3)/(3pi*h^2)
---------
This is the formula for the volume of liquid h units deep in a spherical tank of radius r.
Solving for h is more difficult.
Answer by unlockmath(1688) (Show Source): You can put this solution on YOUR website!
Hello,
Let's go through this. (The book is correct)
v=1/3(pi)h^2(3r-h)
First divide both sides by 1/3(pi)h^2 to get:
v/[1/3(pi)h^2]=(3r-h)
Add h to both sides:
v/[1/3(pi)h^2]+h=3r
Note: the 1/3 could actually be written as:
3v/[(pi)h^2]+h=3r
Now divide each side by 3 to get:
r=3v/3[(pi)h^2]+h/3
Now, we want to combine these two fractions 3v/3[(pi)h^2] and h/3 into one fraction.
To do so we need a common denominator.
Multiply the (h/3) by (pi)h^2]/(pi)h^2] to get:
h(pi)h^2/3[(pi)h^2] or rewritten as:
(pi)h^3/3[(pi)h^2]
Now that we have the same denominator it looks like:
r=3v+(pi)h^3/3(pi)h^2
OK, hope you followed me on this.
Does it make sense to you?
RJ
www.math-unlock.com

RELATED QUESTIONS
I am stuck on thi one!!! Solve for r... (answered by ankor@dixie-net.com,edjones)
solve for h V = (1/3)(pi)(r^2)(h) (answered by unlockmath)
v=1/3 * π*r^(2)*h making h the subject We have this to solve making h the subject: (answered by dnanos)
V = 1/3 Pi r�h = 1/3Pi * 10� *24 = 240 Pi V = 753.98 m� SA = Pi r� + Pi r√2r +... (answered by stanbon)
High school Algebra 2 solve for h: V=1/3pi(rsquared)h Sorry I don't know how to... (answered by mananth)
solve for r and simplify V=[(pi)(r^2)(h)]/(3) V= pi r^2 h _________ (answered by ewatrrr)
Given rt cone height (h) of 12 and radius (r) of 6 find formula for volume in cone as a... (answered by stanbon)
Make R The Subject Of The Formula V=pi... (answered by josgarithmetic)
Solve for h. {{{ V=2(pi)r^2h... (answered by ewatrrr)