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Katarina [22]
3 years ago
10

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.
Mathematics
2 answers:
Sever21 [200]3 years ago
4 0
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 } }
Stels [109]3 years ago
3 0

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.

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