The area (A) of a circle with a radius of r is given by the formula A=pier^2 and its diameter (d) is given by d=2r. Arrange the equations in the correct sequence to rewrite the formula for diameter in terms of the area of the circle.

[tex]A= \pi r^2 \ \ \text{and} \ \ d=2r \ \ \to r= \frac{d}{2} \\ \\ A= \pi *( \frac{d}{2} )^2 \\ \\A= \frac{ \pi d^2}{4} \\ \\ 4A= \pi d^2 \\ \\ d^2= \frac{4A}{ \pi } \\ \\ d= \sqrt{ \frac{4A}{ \pi } } [/tex]

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ApusApus ApusApus · Answer 2 · 2019-03-09T10:26:02+01:00

Answer:

[tex]d=\sqrt{\frac{4A}{\pi}}[/tex]

Step-by-step explanation:

We have been given the formula of area of a circle and we are asked to write the formula of diameter in terms of the area of the circle.

[tex]A=\pi r^2...(1)[/tex]

[tex]d=2r...(2)[/tex]

We will use substitution method to solve for d. From equation (2) we will get,

[tex]\frac{d}{2}=\frac{2r}{2}[/tex]

[tex]\frac{d}{2}=r[/tex]

Upon substituting this value in equation (1) we will get,

[tex]A=\pi (\frac{d}{2})^2[/tex]

[tex]A=\pi *\frac{d^2}{4}[/tex]

Let us multiply both sides of our equation 4.

[tex]A*4=\pi *\frac{d^2}{4}*4[/tex]

[tex]4A=\pi *d^2[/tex]

Let us divide both sides of our equation by pi.

[tex]\frac{4A}{\pi}=\frac{\pi *d^2}{\pi}[/tex]

[tex]\frac{4A}{\pi}=d^2[/tex]

[tex]d^2=\frac{4A}{\pi}[/tex]

Let us take square root of both sides of our equation.

[tex]d=\sqrt{\frac{4A}{\pi}}[/tex]

Therefore, the equation [tex]d=\sqrt{\frac{4A}{\pi}}[/tex] represents the formula for diameter in terms of the area of the circle.