Answer:
The circumference of the circle is 16.
Step-by-step explanation:
Given:
The ratio of the area to the circumference of a circle is 5/4.
Now, to find the circumference of the circle.
So, we get radius(r) first to find circumference.
For, getting radius(r) we use the proportion:
[tex]\frac{Area}{circumference} =\frac{5}{4}[/tex]
Now, putting formula to solve it:
⇒[tex]\frac{\pi r^2}{2\pi r} =\frac{5}{4}[/tex]
On solving we get:
⇒[tex]\frac{r}{2}=\frac{5}{4}[/tex]
By multiplying with 2 on both sides we get:
⇒[tex]r=\frac{5}{4} \times 2[/tex]
⇒[tex]r=\frac{10}{4}[/tex]
⇒[tex]r=2.5.[/tex]
Radius = 2.5.
Now, putting the formula to get the circumference:
[tex]Circumference = 2\pi r[/tex]
Taking the value of π = 3.14.
[tex]Circumference = 2\times 3.14\times 2.5[/tex]
[tex]Circumference = 15.7[/tex]
Circumference = 16 (approximately).
Therefore, the circumference of the circle is 16.
