Final answer:
To find the radius of the circle when the perimeter of a rhombus equals the circle's circumference, calculate the rhombus's perimeter as 4 times a single side (4×11 cm = 44 cm). Then equate this to the circumference of the circle (2πr) and solve for r to get approximately 7 cm.
Step-by-step explanation:
The question asks us to find the radius of a circle when the perimeter of a rhombus is equal to the circumference of the circle, and each side of the rhombus measures 11 cm. To solve this, we start by calculating the perimeter of the rhombus, which is the sum of all its sides.
- Perimeter of rhombus = 4 × side length = 4 × 11 cm = 44 cm
Next, knowing that the perimeter of the rhombus is equal to the circumference of the circle, we set the rhombus's perimeter equal to the circumference formula for a circle, C = 2πr, and solve for r, the radius of the circle.
- Circumference of the circle (C) = Perimeter of rhombus = 44 cm
- 44 cm = 2πr
- r = 44 cm / (2π)
Dividing both sides by 2π, we determine the radius:
- r = 44 cm / (2 × 3.14159...)
- r ≈ 7 cm
The approximate radius of the circle is 7 cm.