Answer:
Diameter of pound = 10 yd
Step-by-step explanation:
Given area of circular pond = 78.5 square yd
To find the diameter of the pond.
Solution:
The pond being circular in shape, the area of pond can be given as:
⇒ [tex]\pi\ r^2[/tex]
where [tex]r[/tex] represents radius of the pond.
Thus, we have:
⇒ [tex]\pi\ r^2=78.5[/tex]
Using [tex]\pi=3.14[/tex]
⇒ [tex]3.14r^2=78.5[/tex]
Solving for [tex]r[/tex]
Dividing both sides by 3.14
⇒ [tex]\frac{3.14r^2}{3.14}=\frac{78.5}{3.14}[/tex]
⇒ [tex]r^2=25[/tex]
Taking square root both sides.
⇒ [tex]\sqrt{r^2}=\sqrt{25}[/tex]
⇒ [tex]r=\pm5[/tex]
So, radius = 5 yd, as distances are always positive.
Diameter = [tex]2\times radius=2\times 5\ yd= 10\ yd[/tex]
Thus, diameter of pound = 10 yd
