A wire bent into a square encloses 484 sq cm. If reshaped into a circle, what area will it enclose_________?
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Answer: C. 616 Sq.cm
Explanation
A square enclosing four hundred eighty four square centimeters has a side length of twenty two centimeters. Calculating the total perimeter of the square yields eighty eight centimeters of total wire length. Bending the wire into a circle creates a circumference of eighty eight centimeters giving a radius of fourteen. The perimeter of a geometric shape remains constant when the wire is reshaped into a different figure. A circle circumference formula equals two times pi multiplied by the radius length. The area of a circle is calculated by multiplying pi by the square of its radius.
Metalworking and manufacturing industries calculate material lengths required when reshaping wire components. Geometric transformations demonstrate how perimeter conservation affects area measurements across shapes. Architectural design uses circular and rectangular perimeter calculations for fencing and framing. Option A suggests four eighty four square units which incorrectly assumes the area remains unchanged. Option B proposes five hundred thirty eight and two sevenths square centimeters due to calculation error. Option D offers six hundred forty four square centimeters which overestimates the circular area.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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