Answer :
To find the diameter of a circle with an area of 361π square meters, you first need to understand the formula for the area of a circle:
Area (A) = π * radius^2.
Here, the area is given as 361π, so we need to solve for the radius (r) first. To do so, we can rearrange the formula to solve for r:
radius^2 = Area / π.
Now, plug in the values:
radius^2 = (361π) / π.
Since π in the numerator and denominator cancel each other out, the equation simplifies to:
radius^2 = 361.
Next, we take the square root of both sides to solve for the radius:
radius = √361.
Since 361 is a perfect square (19^2), we find that:
radius = 19 meters.
Now, we are looking for the diameter, which is twice the radius. The formula for the diameter (D) of a circle is:
Diameter (D) = 2 * radius.
Here, we know the radius is 19 meters. So,
Diameter = 2 * 19 = 38 meters.
Therefore, the diameter of the circle is 38 meters.
