Problem:
A rhombus has the same perimeter as the circumference of a circle. If each side of the rhombus measures 33 cm, find the radius of the circle.

Solution:

To find the radius of the circle, we need to understand the properties of a rhombus and a circle and then apply the given information to solve the problem.

Rhombus Properties:
1. A rhombus is a quadrilateral with all sides of equal length.
2. Opposite angles of a rhombus are equal.
3. Diagonals of a rhombus bisect each other at right angles.

Circle Properties:
1. The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius of the circle.

Given Information:
1. Each side of the rhombus measures 33 cm.
2. The perimeter of the rhombus is equal to the circumference of the circle.

Now, let's solve the problem step by step:

Step 1:
Find the perimeter of the rhombus by multiplying the length of one side by 4.
Perimeter of the rhombus = 33 cm x 4 = 132 cm

Step 2:
Since the perimeter of the rhombus is equal to the circumference of the circle, we can equate them.
Circumference of the circle = 132 cm

Step 3:
Use the formula for the circumference of a circle to find the radius.
C = 2πr
132 = 2πr

Step 4:
Simplify the equation by dividing both sides by 2π.
132/(2π) = r

Step 5:
Calculate the value of r using a calculator.
r ≈ 21 cm

Answer:
The radius of the circle is approximately 21 cm.