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Difficulty: EasyCircular Area and Circumference Applications

A homeowner is planning to paint a circular concrete patio. The patio has a diameter of 66 meters. What is the total area of the patio that needs to be painted? (Use π=3.14\pi = 3.14)

  1. A
    9.429.42 square meters
  2. B
    18.8418.84 square meters
  3. 28.2628.26 square metersAnswer
  4. D
    113.04113.04 square meters

Answer

The correct area that needs to be painted is 28.2628.26 square meters.
The correct answer is found by first determining the radius, which is half of the diameter (6÷2=36 \div 2 = 3 meters). Next, substitute the radius into the area formula A=π×r2A = \pi \times r^2. Squaring the radius gives 32=93^2 = 9. Multiplying by π\pi gives 3.14×9=28.263.14 \times 9 = 28.26 square meters.

Step-by-Step Solution

1
Find the radius of the circular patio from the given diameter.
r=6÷2=3r = 6 \div 2 = 3 meters
The area formula requires the radius, which is exactly half of the diameter.
2
Identify the formula for the area of a circle.
A=π×r2A = \pi \times r^2
The problem asks for the total surface area to be painted.
3
Substitute the radius and the given value of π\pi into the area formula and solve.
A=3.14×(3)2=3.14×9=28.26A = 3.14 \times (3)^2 = 3.14 \times 9 = 28.26 square meters
This calculation provides the final area in square meters.

Key Concept

Calculating the area of a circle given its diameter.
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Topics

Circular Area and Circumference Applications

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