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
Algebra ->
Polynomials-and-rational-expressions
-> 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
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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)
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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.
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
