Digital SATMath: Geometry and TrigonometryEasy
A landscaper is designing a circular garden with a radius of 6 feet. They plan to install a decorative border around the entire perimeter of the garden. If the border material costs $2.50 per foot, what is the total cost of the border?
- A$94.20
- B$188.40
- C$47.10
- D$113.04
Show answer & explanationAnswer & explanation
Correct answer: A. $94.20
The total cost is found by calculating the circumference of the circular garden and then multiplying it by the cost per foot. Circumference (C) = 2πr = 2 * π * 6 = 12π feet. Cost = 12π * $2.50 = $30π ≈ $94.25. Option B is the closest approximation.
Why the other options are wrong
- B. This is roughly double the correct cost, perhaps from squaring the radius or other calculation errors.
- C. This would be the cost if the radius was the circumference, which is incorrect.
- D. This might result from using the area instead of circumference or an incorrect radius.
Circumference of a Circle
The distance around the edge of a circle.
- Formula: C = 2πr (where r is the radius)
- Formula: C = πd (where d is the diameter)
- Used to measure the perimeter of circular objects
Memory trick: Circumference is like a fence, around the whole place.