# Solve for r V=1/3*(pir^2h)

V=13⋅(πr2h)
Rewrite the equation as 13⋅(πr2h)=V.
13⋅(πr2h)=V
Multiply both sides of the equation by 113⋅π.
113⋅π⋅13⋅(πr2h)=113⋅πV
Simplify both sides of the equation.
Simplify 113⋅π⋅13⋅(πr2h).
Combine 13 and π.
1π3⋅13⋅(πr2h)=113⋅πV
Multiply the numerator by the reciprocal of the denominator.
13π⋅13⋅(πr2h)=113⋅πV
Multiply 3π by 1.
3π⋅13⋅(πr2h)=113⋅πV
Cancel the common factor of 3.
Cancel the common factor.
3π⋅13⋅(πr2h)=113⋅πV
Rewrite the expression.
1π⋅(πr2h)=113⋅πV
1π⋅(πr2h)=113⋅πV
Cancel the common factor of π.
Factor π out of πr2h.
1π⋅(π(r2h))=113⋅πV
Cancel the common factor.
1π⋅(π(r2h))=113⋅πV
Rewrite the expression.
r2h=113⋅πV
r2h=113⋅πV
r2h=113⋅πV
Simplify 113⋅πV.
Combine 13 and π.
r2h=1π3V
Multiply the numerator by the reciprocal of the denominator.
r2h=13πV
Multiply 3π by 1.
r2h=3πV
Combine 3π and V.
r2h=3Vπ
r2h=3Vπ
r2h=3Vπ
Divide each term by h and simplify.
Divide each term in r2h=3Vπ by h.
r2hh=3Vπ⋅1h
Cancel the common factor of h.
Cancel the common factor.
r2hh=3Vπ⋅1h
Divide r2 by 1.
r2=3Vπ⋅1h
r2=3Vπ⋅1h
Multiply 3Vπ and 1h.
r2=3Vπh
r2=3Vπh
Take the square root of both sides of the equation to eliminate the exponent on the left side.
r=±3Vπh
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Rewrite 3Vπh as 3Vπh.
r=±3Vπh
Multiply 3Vπh by πhπh.
r=±3Vπh⋅πhπh
Combine and simplify the denominator.
Multiply 3Vπh and πhπh.
r=±3Vπhπhπh
Raise πh to the power of 1.
r=±3Vπhπhπh
Raise πh to the power of 1.
r=±3Vπhπhπh
Use the power rule aman=am+n to combine exponents.
r=±3Vπhπh1+1
Add 1 and 1.
r=±3Vπhπh2
Rewrite πh2 as πh.
Use axn=axn to rewrite πh as (πh)12.
r=±3Vπh((πh)12)2
Apply the power rule and multiply exponents, (am)n=amn.
r=±3Vπh(πh)12⋅2
Combine 12 and 2.
r=±3Vπh(πh)22
Cancel the common factor of 2.
Cancel the common factor.
r=±3Vπh(πh)22
Divide 1 by 1.
r=±3Vπhπh
r=±3Vπhπh
Simplify.
r=±3Vπhπh
r=±3Vπhπh
r=±3Vπhπh
Combine using the product rule for radicals.
r=±3Vπhπh
r=±3Vπhπh
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the ± to find the first solution.
r=3Vπhπh
Next, use the negative value of the ± to find the second solution.
r=-3Vπhπh
The complete solution is the result of both the positive and negative portions of the solution.
r=3Vπhπh
r=-3Vπhπh
r=3Vπhπh
r=-3Vπhπh
r=3Vπhπh
r=-3Vπhπh
Solve for r V=1/3*(pir^2h)

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