A circular piece of thin wire is bent and converted into a rhombus of side 11 cm. Assuming the wire length remains the same and there is no wastage, find the diameter of the original circular wire in cm, using pi = 22/7 for calculation consistency.

Introduction / Context:This question tests the conservation of perimeter (or total wire length) when a wire is reshaped. The wire initially forms a circle, so its length is the circle’s circumference. After reshaping into a rhombus, the same wire length becomes the rhombus perimeter. So, equate circumference of the circle to the perimeter of the rhombus and solve for the circle’s diameter.

Given Data / Assumptions:

• Rhombus side = 11 cm
• Perimeter of rhombus = 4 * side
• Circle wire length = circumference = pi * diameter
• No stretching or wastage, so lengths are equal
• Use pi = 22/7

Concept / Approach:Compute rhombus perimeter, set it equal to circle circumference, then solve for diameter = (perimeter)/pi.

Step-by-Step Solution:

Verification / Alternative check:If diameter is 14 cm, circumference = pi*d = (22/7)*14 = 44 cm, exactly matching the rhombus perimeter 44 cm. Since wire length is conserved, this confirms the answer.

Why Other Options Are Wrong:

Common Pitfalls:Common mistakes include equating circumference to 2*pi*r but then forgetting to convert to diameter, or using area formulas instead of perimeter/circumference. Another pitfall is assuming the rhombus side equals the circle radius or diameter, which is not implied. Always use the “same wire length” conservation idea.

Final Answer:14 cm