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Question

Difficulty: MediumCircles

A circular track has an inner circumference of 440440 meters. The track has a uniform width of 77 meters. What is the circumference of the outer edge of the track? (Use π≈227\pi \approx \frac{22}{7})

  1. A
    447 meters
  2. B
    462 meters
  3. 484 metersAnswer
  4. D
    528 meters

Answer

484 meters
The inner circumference is 440440 meters. Using the formula C=2πrC = 2\pi r, the inner radius is 7070 meters (440=2×227×r440 = 2 \times \frac{22}{7} \times r). Because the track has a uniform width of 77 meters, the outer radius is 70+7=7770 + 7 = 77 meters. Using the circumference formula again for the outer edge, C=2×227×77=484C = 2 \times \frac{22}{7} \times 77 = 484 meters.

Step-by-Step Solution

1
Find the inner radius using the given circumference.
rinner=70r_{inner} = 70 meters
Using the formula C=2πrC = 2\pi r, substitute 440440 for CC and 227\frac{22}{7} for π\pi: 440=2×227×r440 = 2 \times \frac{22}{7} \times r, which simplifies to r=70r = 70.
2
Calculate the outer radius by adding the track's width.
router=77r_{outer} = 77 meters
The outer edge is 77 meters further from the center than the inner edge, so you must add the width to the inner radius (70+7=7770 + 7 = 77).
3
Calculate the outer circumference.
484484 meters
Use the formula C=2πrC = 2\pi r with the new outer radius: C=2×227×77=44×11=484C = 2 \times \frac{22}{7} \times 77 = 44 \times 11 = 484.

Key Concept

Calculating the circumference of concentric circles by determining and adjusting their respective radii.

Alternative Method

You can also solve this using the diameter. The inner diameter is 140140 meters (440=πd440 = \pi d). Since the track is 77 meters wide on all sides, the total width added to the overall diameter is 1414 meters (7×27 \times 2). The outer diameter is 140+14=154140 + 14 = 154 meters. The outer circumference is 227×154=484\frac{22}{7} \times 154 = 484 meters.
Estimated Time:1m 30s
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Topics

Circles

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