How to find the ratio of diameter and circumference

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Math › How to find the ratio of diameter and circumference

Questions 1 - 10

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

$2\pi :1$

$\pi :1$

$\pi ^{2}:1$

Undefined.

Explanation

The circumference of any circle is

$2\pi*r$

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

$\frac{2\pi*r}{r}$

$=2\pi$

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

$\pi$

$2\pi$

$\frac{\pi}{2}$

Explanation

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 .

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

$\frac{1}{\pi}$

$\pi$

$D\pi$

$\frac{\pi}{C}$

Explanation

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 $\frac{1}{\pi}$ .

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

$\frac{C^2}{\pi}$

$\frac{C^2}{4\pi}$

$\frac{C}{4\pi}$

$\frac{\pi C^2}{4}$

Explanation

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:

$A=\pi r^2$

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

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

$=C^2/4\pi$

In the game of Sumo, both wrestlers are placed on the outer edge of the ring, on opposite sides of each other. If the wrestling ring is a perfect circle and has an area of , what would be the distance between both wrestlers?

Explanation

With the two wrestlers standing opposite each other on the edge of the ring, the distance between them would constitute the diameter of the circle. We can use the formula for circular area to find the diameter:

$\area=\pi\cdot r^2\ \804.25;ft^2=3.14159\cdot r^2\ \r^2=\frac{804.25;ft^2}{3.14159}=256;ft^2\ \radius=\sqrt{256;ft^2}=16;ft\ \diameter=2\cdot16;ft=32;ft$

The diameter of a certain circle is tripled. Compared to the circumference of the original circle, how many times as large is the circumference of the new circle?

$3\pi$

$9\pi$

Explanation

The easiest way to find our answer is to try actual values. Imagine we have a circle with a diameter of . Given the formula for circumference

$C=d\pi$

our circumference is simply $2\pi$ . Tripling the diameter gives a new diameter of and therefore a new circumference of $6\pi$ . We can then determine the ratio between the two circumferences.

$\frac{6\pi}{2\pi}=3$

Therefore, the new circumference is 3 times as large as the old.

What is the circumference to diameter ratio of a circle with a diameter of 15?

Cannot be determined.

Explanation

First you must find the circumference of a circle with a diameter of 15 with the formula $C=\pi*D$ .

$C=\pi*15=47.1$

Since the ratio of C to D is represented by $\pi=\frac{C}{D}$ , all of the ratios of Circumference to Diameter should approximately equal $\pi$ .

$\frac{47.1}{15}=3.14$

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

$\frac{C^2}{\pi}$

$\frac{C^2}{4\pi}$

$\frac{C}{4\pi}$

$\frac{\pi C^2}{4}$

Explanation

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:

$A=\pi r^2$

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

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

$=C^2/4\pi$

A can of soup has a base area of $16\pi$ . What is the ratio of the can's diameter to its circumference?