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 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 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

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)