The circumference is 46.5 cm. Find the area of the circle bounded by this circle.

1) Calculate the radius of the circle.
A circle is a flat geometric figure whose points are equidistant from a given point, the center of the circle.
Let’s write the formula for calculating the circumference:
l = 2πR,
where l is the circumference, R is the radius, π = 3.14.
Let us express the radius of the circle from the formula:
R = l / 2π.
Substituting the known values ​​of the circumference and constant π into the formula, we find the radius of the circle:
R = l / 2π,
R = 46.5 / (2 × 3.14) = 46.5 / 6.28 = 7.4 cm.
2) Calculate the area of ​​a circle bounded by a given circle.
A circle is a locus of points on a plane equidistant from a given point, which is called the center of a circle.
Let’s write a formula for calculating the area of ​​a circle:
S = πR²,
Substitute the radius of the circle, the constant π, into the formula and calculate the area:
S = 3.14 × 7.4² = 3.14 × 54.76 = 171.95 cm².
Answer: the area of ​​the circle is 171.95 cm².