To determine the diameter and circumference of a circular playground with an area of [tex]\(153.86 \, m^2\)[/tex], given [tex]\(\pi = 3.14\)[/tex], we can follow these steps:
### Step 1: Determine the Radius
The formula for the area [tex]\(A\)[/tex] of a circle is given by:
[tex]\[ A = \pi r^2 \][/tex]
where [tex]\(r\)[/tex] is the radius of the circle.
Given that the area [tex]\(A\)[/tex] is [tex]\(153.86 \, m^2\)[/tex], we can solve for [tex]\(r\)[/tex] as follows:
[tex]\[ 153.86 = 3.14 \cdot r^2 \][/tex]
To isolate [tex]\(r^2\)[/tex], we divide both sides by [tex]\(\pi\)[/tex]:
[tex]\[ r^2 = \frac{153.86}{3.14} \][/tex]
[tex]\[ r^2 = 49 \][/tex]
Taking the square root of both sides, we find the radius [tex]\(r\)[/tex]:
[tex]\[ r = \sqrt{49} \][/tex]
[tex]\[ r = 7 \, m \][/tex]
### Step 2: Determine the Diameter
The diameter [tex]\(D\)[/tex] of a circle is twice the radius. Hence:
[tex]\[ D = 2r \][/tex]
Substituting the value of [tex]\(r\)[/tex]:
[tex]\[ D = 2 \times 7 \][/tex]
[tex]\[ D = 14 \, m \][/tex]
### Step 3: Determine the Circumference
The circumference [tex]\(C\)[/tex] of a circle is given by:
[tex]\[ C = 2\pi r \][/tex]
Substituting the values for [tex]\(\pi\)[/tex] and [tex]\(r\)[/tex]:
[tex]\[ C = 2 \times 3.14 \times 7 \][/tex]
[tex]\[ C = 43.96 \, m \][/tex]
### Summary
For a circular playground with an area of [tex]\(153.86 \, m^2\)[/tex]:
- The diameter of the plastered part is [tex]\(14 \, m\)[/tex].
- The circumference is [tex]\(43.96 \, m\)[/tex].
