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Question

Difficulty: EasyCircles

A circular hatch on a maritime vessel has a diameter of 1414 inches. What is the area of the hatch in square inches?

  1. A
    14π14\pi
  2. B
    28π28\pi
  3. 49π49\piAnswer
  4. D
    196π196\pi

Answer

The correct area is 49π49\pi square inches.
The correct answer is found by first determining the radius, which is half of the given diameter (14÷2=714 \div 2 = 7 inches). Applying the area formula A=πr2A = \pi r^2 yields π×72=49π\pi \times 7^2 = 49\pi square inches.

Step-by-Step Solution

1
Determine the radius of the circular hatch.
Radius = 14÷2=714 \div 2 = 7 inches.
The formula for the area of a circle requires the radius, which is exactly half of the diameter.
2
Apply the area formula for a circle.
Area = π×72=49π\pi \times 7^2 = 49\pi square inches.
The area of a circle is found using the formula A=πr2A = \pi r^2.

Key Concept

Calculating the area of a circle by first deriving the radius from the diameter.
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Topics

Circles

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