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Question

Difficulty: EasyCircles

A landscaper is placing a decorative border around a circular flower bed. The radius of the flower bed is 1212 feet. What is the total length of the border needed in terms of π\pi?

  1. 24π24\pi feetAnswer
  2. B
    12π12\pi feet
  3. C
    144π144\pi feet
  4. D
    576π576\pi feet

Answer

The total length of the border is 24π24\pi feet, which is found by calculating the circumference of the circle.
To find the total length of the border, you must calculate the circumference of the circular flower bed. The formula for circumference is C=2πrC = 2\pi r. Substituting the given radius of 1212 feet into the formula gives C=2⋅π⋅12=24πC = 2 \cdot \pi \cdot 12 = 24\pi feet.

Step-by-Step Solution

1
Identify the mathematical concept required to find the length of a border around a circle.
The length of the border corresponds to the circumference of the circle.
Perimeter (circumference) measures the distance around the outside of a 2D shape.
2
Select the correct formula for the circumference of a circle.
Formula: C=2πrC = 2\pi r
The problem provides the radius (rr), so this is the most direct formula to use.
3
Substitute the given radius value into the formula and solve.
C=2⋅π⋅12=24πC = 2 \cdot \pi \cdot 12 = 24\pi feet.
Replacing rr with 1212 computes the exact circumference in terms of π\pi.

Key Concept

Circumference of a circle
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Topics

Circles

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