GRE General TestQuantitative ReasoningMedium
A gardener is designing a circular flower bed with a radius of 7 feet. He wants to install a decorative border around the edge. If the border material costs $3 per linear foot, and pi (π) is approximated as 22/7, what will be the total cost of the border?
- A$132
- B$147
- C$462
- D$66
Show answer & explanationAnswer & explanation
Correct answer: A. $132
The circumference of a circle is C = 2 * π * r. Given r = 7 feet and π ≈ 22/7, the circumference is C = 2 * (22/7) * 7 = 2 * 22 = 44 feet. The total cost is the circumference multiplied by the cost per linear foot: 44 feet * $3/foot = $132.
Why the other options are wrong
- B. This is incorrect; it might be related to the area or a miscalculation.
- C. This is the area of the circle (πr^2) multiplied by the cost, which is incorrect as the border is around the edge (circumference).
- D. This is (π * r) * cost, which is half the circumference, incorrect.
Circumference of a Circle
The circumference of a circle is the total distance around its boundary, analogous to the perimeter of a polygon.
- Formula: C = 2 * π * r or C = π * d (where d is diameter).
- π (pi) is a mathematical constant, approximately 3.14159 or 22/7.
- Units of circumference are linear (e.g., feet, meters).
Memory trick: Circumference is the 'circle's perimeter', then multiply by the 'price tag'.