Question

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.

Answer 1

$A= \pi r^2 \ \ \text{and} \ \ d=2r \ \ \to r= \frac{d}{2} \\ \\ A= \pi *( \frac{d}{2} )^2 \\ \\A= \frac{ \pi d^2}{4} \\ \\ 4A= \pi d^2 \\ \\ d^2= \frac{4A}{ \pi } \\ \\ d= \sqrt{ \frac{4A}{ \pi } }$

Answer 2

Answer:

$d=\sqrt{\frac{4A}{\pi}}$

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.

$A=\pi r^2...(1)$

$d=2r...(2)$

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

$\frac{d}{2}=\frac{2r}{2}$

$\frac{d}{2}=r$

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

$A=\pi (\frac{d}{2})^2$

$A=\pi *\frac{d^2}{4}$

Let us multiply both sides of our equation 4.

$A*4=\pi *\frac{d^2}{4}*4$

$4A=\pi *d^2$

Let us divide both sides of our equation by pi.

$\frac{4A}{\pi}=\frac{\pi *d^2}{\pi}$

$\frac{4A}{\pi}=d^2$

$d^2=\frac{4A}{\pi}$

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

$d=\sqrt{\frac{4A}{\pi}}$

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