Question

Write the ratio of the area of a circle with radius r to the circumference of the same circle

Answer 1

Answer:

$\frac{r}{2\pi r} =\frac{1}{2\pi }$

Step-by-step explanation:

A ratio is a comparison of two quantities and can be written in several forms including fractions. It is most commonly written in fraction form or a:b.

To write a ratio, we count the number of each quantity we are comparing or use the variable for that quantity. We write radius:circumference. Recall, the circumference of a circle can be found using $\pi d$ or $2\pi r$.

We write r: $\pi d$  or r:$2\pi r$.

We can also write in fraction form:

$\frac{r}{\pi d}$ or $\frac{r}{2\pi r} =\frac{1}{2\pi }$

Answer 2

You can use the fact that ratio of one quantity to other is fraction involving one quantity over another quantity.

The specified ratio is given as

$r:2\\\\or\\\\\dfrac{r}{2}$

What is the ratio of a to b ?

The ratio of a to b is  $\dfrac{a}{b}$

It is sometimes written as $a:b$

We can remove common factors of a and b to simplify them.

Thus, if

$a = c \times x\\b = d \times x$
then

$\dfrac{a}{b} = \dfrac{c \times x}{d \times x} = \dfrac{c}{d}$

What is the area of a circle and circumference of a circle with radius r units?

The area of a circle with radius r units is

$Area = \pi r^2$

The circumference of a circle with radius r units is

$Circumference = 2 \pi r$

( Remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in $2 \times x = 2x$ )

Their ratio is

$\dfrac{Area_r}{Circumference_r} = \dfrac{\pi r^2}{2\pi r} = \dfrac{r}{2}$

Thus,

The specified ratio is given as

$r:2\\\\or\\\\\dfrac{r}{2}$

Learn more about ratio here:

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