How to find the ratio of diameter and circumference - High School Math

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Question

Let represent the area of a circle and represent its circumference. Which of the following equations expresses in terms of ?

Answer

The formula for the area of a circle is $A=\pi r^2$ , and the formula for circumference is $C=2\pi r$ . If we solve for C in terms of r, we get
$r=C/2\pi$ .

We can then substitute this value of r into the formula for the area:

$A=\pi r^2$

$=\pi (C/2\pi )^2$

$=C^2\pi /4\pi ^2$

$=C^2/4\pi$

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Question

What is the ratio of the diameter of a circle to the circumference of the same circle?

Answer

To find the ratio we must know the equation for the circumference of a circle. In this equation, is the circumference and is the diameter.

$C=D\pi$

Once we know the equation, we can solve for the ratio of the diameter to circumference by solving the equation for $\frac{D}{C}$ . We do this by dividing both sides by .

$\frac{C}{\pi}=\frac{D\pi}{\pi}$

$\frac{C}{\pi}=D$

Then we divide both sides by the circumference.

$\frac{C}{\pi C}=\frac{1}{\pi}=\frac{D}{C}$

We now know that the ratio of the diameter to circumference is equal to $\frac{1}{\pi}$ .

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Question

What is the ratio of the diameter and circumference of a circle?

Answer

To find the ratio we must know the equation for the circumference of a circle is

$Circumference=\pi d$

Once we know the equation we can solve for the ratio of the diameter to circumference by solving the equation for $\frac{diameter}{Circumference}$

we divide both sides by the circumference giving us

$\frac{d}{\pi d}=\frac{1}{\pi }$

We now know that the ratio of the diameter to circumference is equal to .

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Question

What is the ratio of any circle's circumference to its radius?

Answer

The circumference of any circle is

$2\pir$

So the ratio of its circumference to its radius r, is

$\frac{2\pir}{r}$

$=2\pi$

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