Question

The area (A) of a circle with a radius of ris given by the formula A = 772 and its diameter (d) is given by d = 27. Arrange the equations in the correct
sequence to rewrite the formula for diameter in terms of the area of the circle.

Answer 1

The correct sequence is:

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

Further explanation:

We know that the formula for area of circle is:

$A=\pi r^2$

We have to write the formula for d using the area's formula

As we know that

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

Putting r=d/2 in area's formula

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

$d^2=\frac{4A}{\pi }\\Taking\ square\ root\ on\ both\ sides\\\sqrt{d^2} = \sqrt{\frac{4A}{\pi }}\\d=\sqrt{\frac{4A}{\pi }$

Keywords: Area of circle, diameter

Learn more about area of circle at:

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