Solve for d A=1/4pid^2

$A = \frac{1}{4} π d^{2}$

Step 1

Rewrite the equation as $\frac{1}{4} \cdot (π d^{2}) = A$ .

$\frac{1}{4} \cdot (π d^{2}) = A$

Step 2

Multiply both sides of the equation by $\frac{1}{\frac{1}{4} π}$ .

$\frac{1}{\frac{1}{4} π} (\frac{1}{4} \cdot (π d^{2})) = \frac{1}{\frac{1}{4} π} A$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{1}{\frac{1}{4} π} (\frac{1}{4} \cdot (π d^{2}))$ .

Combine $\frac{1}{4}$ and $π$ .

$\frac{1}{\frac{π}{4}} (\frac{1}{4} \cdot (π d^{2})) = \frac{1}{\frac{1}{4} π} A$

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{4}{π} (\frac{1}{4} \cdot (π d^{2})) = \frac{1}{\frac{1}{4} π} A$

Multiply $\frac{4}{π}$ by $1$ .

$\frac{4}{π} (\frac{1}{4} \cdot (π d^{2})) = \frac{1}{\frac{1}{4} π} A$

Cancel the common factor of $π$ .

Factor $π$ out of $\frac{1}{4} \cdot (π d^{2})$ .

$\frac{4}{π} (π (\frac{1}{4} \cdot (d^{2}))) = \frac{1}{\frac{1}{4} π} A$

Cancel the common factor.

$\frac{4}{π} (π (\frac{1}{4} \cdot (d^{2}))) = \frac{1}{\frac{1}{4} π} A$

Rewrite the expression.

$4 (\frac{1}{4} \cdot (d^{2})) = \frac{1}{\frac{1}{4} π} A$

Combine $\frac{1}{4}$ and $d^{2}$ .

$4 \frac{d^{2}}{4} = \frac{1}{\frac{1}{4} π} A$

Combine $4$ and $\frac{d^{2}}{4}$ .

$\frac{4 d^{2}}{4} = \frac{1}{\frac{1}{4} π} A$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 d^{2}}{4} = \frac{1}{\frac{1}{4} π} A$

Divide $d^{2}$ by $1$ .

$d^{2} = \frac{1}{\frac{1}{4} π} A$

Simplify the right side.

Simplify $\frac{1}{\frac{1}{4} π} A$ .

Combine $\frac{1}{4}$ and $π$ .

$d^{2} = \frac{1}{\frac{π}{4}} A$

Multiply the numerator by the reciprocal of the denominator.

$d^{2} = 1 \frac{4}{π} A$

Multiply $\frac{4}{π}$ by $1$ .

$d^{2} = \frac{4}{π} A$

Combine $\frac{4}{π}$ and $A$ .

$d^{2} = \frac{4 A}{π}$

Step 4

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$d = \pm \sqrt{\frac{4 A}{π}}$

Step 5

Simplify $\pm \sqrt{\frac{4 A}{π}}$ .

Rewrite $\sqrt{\frac{4 A}{π}}$ as $\frac{\sqrt{4 A}}{\sqrt{π}}$ .

$d = \pm \frac{\sqrt{4 A}}{\sqrt{π}}$

Simplify the numerator.

Rewrite $4$ as $2^{2}$ .

$d = \pm \frac{\sqrt{2^{2} A}}{\sqrt{π}}$

Pull terms out from under the radical.

$d = \pm \frac{2 \sqrt{A}}{\sqrt{π}}$

Multiply $\frac{2 \sqrt{A}}{\sqrt{π}}$ by $\frac{\sqrt{π}}{\sqrt{π}}$ .

$d = \pm \frac{2 \sqrt{A}}{\sqrt{π}} \cdot \frac{\sqrt{π}}{\sqrt{π}}$

Combine and simplify the denominator.

Multiply $\frac{2 \sqrt{A}}{\sqrt{π}}$ by $\frac{\sqrt{π}}{\sqrt{π}}$ .

$d = \pm \frac{2 \sqrt{A} \sqrt{π}}{\sqrt{π} \sqrt{π}}$

Raise $\sqrt{π}$ to the power of $1$ .

$d = \pm \frac{2 \sqrt{A} \sqrt{π}}{{\sqrt{π}}^{1} \sqrt{π}}$

Raise $\sqrt{π}$ to the power of $1$ .

$d = \pm \frac{2 \sqrt{A} \sqrt{π}}{{\sqrt{π}}^{1} {\sqrt{π}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$d = \pm \frac{2 \sqrt{A} \sqrt{π}}{{\sqrt{π}}^{1 + 1}}$

Add $1$ and $1$ .

$d = \pm \frac{2 \sqrt{A} \sqrt{π}}{{\sqrt{π}}^{2}}$

Rewrite ${\sqrt{π}}^{2}$ as $π$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{π}$ as $π^{\frac{1}{2}}$ .

$d = \pm \frac{2 \sqrt{A} \sqrt{π}}{{(π^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$d = \pm \frac{2 \sqrt{A} \sqrt{π}}{π^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$d = \pm \frac{2 \sqrt{A} \sqrt{π}}{π^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$d = \pm \frac{2 \sqrt{A} \sqrt{π}}{π^{\frac{2}{2}}}$

Rewrite the expression.

$d = \pm \frac{2 \sqrt{A} \sqrt{π}}{π^{1}}$

Simplify.

$d = \pm \frac{2 \sqrt{A} \sqrt{π}}{π}$

Combine using the product rule for radicals.

$d = \pm \frac{2 \sqrt{π A}}{π}$

Step 6

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$d = \frac{2 \sqrt{π A}}{π}$

Next, use the negative value of the $\pm$ to find the second solution.

$d = - \frac{2 \sqrt{π A}}{π}$

The complete solution is the result of both the positive and negative portions of the solution.

$d = \frac{2 \sqrt{π A}}{π}$

$d = - \frac{2 \sqrt{π A}}{π}$

$d = \frac{2 \sqrt{π A}}{π}$

$d = - \frac{2 \sqrt{π A}}{π}$

Solve for d A=1/4pid^2

Related Questions

Support LCMGCF.com by disabling your adblocker.