Question

If a circle has a circumference of 46, what is the radius?
i would have thought it was 7.3 ( rounded) but i have been told that is wrong.

Answer 1

Answer:

$\boxed{r = \dfrac{23}{\pi}}$

$\boxed{r \approx 7.32}$

Step-by-step explanation:

The definition of circumference is:

$C = \pi d$

where:

• $d$ = diameter
• $\pi$ = pi, approximately 3.14

We also know that the radius of a circle is:

$r = \dfrac{1}{2}d$

Solving for $d$ by plugging the given information into the circumference definition:

$46 = \pi d$

$\dfrac{46}{\pi} = d$

Then, using that to solve for radius:

$r = \dfrac{1}{2}\left(\dfrac{46}{\pi}\right)$

$\boxed{r = \dfrac{23}{\pi}}$

$\boxed{r \approx 7.32}$