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Zorluk: OrtaPerimeter and Area of 2D Figures

A circular fountain has a diameter of 1212 meters and is surrounded by a paved walkway that is 33 meters wide. Which of the following represents the area of the walkway in square meters?

  1. A
    180π180\pi
  2. B
    81π81\pi
  3. 45π45\piCevap
  4. D
    6π6\pi

Cevap

The correct answer is 45π45\pi.
The correct answer is found by subtracting the area of the inner circle from the area of the larger outer circle. The inner radius is 66 meters (half of the 1212-meter diameter), giving an area of 36π36\pi. The outer radius is 99 meters (66 meters plus the 33-meter walkway), giving a total area of 81π81\pi. The difference is 81π−36π=45π81\pi - 36\pi = 45\pi.

Adım Adım Çözüm

1
Find the radius of the inner fountain.
12÷2=612 \div 2 = 6 meters.
The area formula for a circle requires the radius, which is half of the diameter.
2
Calculate the area of the fountain.
Area = π×62=36π\pi \times 6^2 = 36\pi square meters.
This establishes the area of the space not covered by the walkway.
3
Find the radius of the total circular area (fountain plus walkway).
6+3=96 + 3 = 9 meters.
The walkway adds 33 meters to the radius of the inner circle.
4
Calculate the total area.
Area = π×92=81π\pi \times 9^2 = 81\pi square meters.
This gives the combined area of both the fountain and the walkway.
5
Subtract the fountain's area from the total area.
81π−36π=45π81\pi - 36\pi = 45\pi square meters.
Subtracting the inner area isolates the area of just the paved walkway.

Anahtar Kavram

To find the area of a ring (annulus), calculate the area of the outer circle and subtract the area of the inner circle.
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Perimeter and Area of 2D Figures

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