Question

what is the approximate area of the circle shown below?

a. \\(1018\text{ cm}^2\\)
b. \\(28.3\text{ cm}^2\\)
c. \\(254\text{ cm}^2\\)
d. \\(56.5\text{ cm}^2\\)

Explanation:

Identify the given diameter

Using the Diameter of a Circle knowledge point

$$ d = 18\text{ cm} $$

Calculate the radius

Using the Radius of a Circle knowledge point

$$ r = \frac{d}{2} = \frac{18}{2} = 9\text{ cm} $$

Calculate the area of the circle

We use the area formula to find the region enclosed by the circle.

$$ A = \pi r^2 $$

$$ A = \pi (9)^2 = 81\pi\text{ cm}^2 $$

Approximate the numerical value

We use the approximation \(\pi \approx 3.14159\) to find the decimal value.

$$ A \approx 81 \times 3.14159 \approx 254.47\text{ cm}^2 $$

This rounds to approximately \(254\text{ cm}^2\).

Answer:

• A. \(1018\text{ cm}^2\)
• B. \(28.3\text{ cm}^2\)
• C. \(254\text{ cm}^2\) (Correct answer)
• D. \(56.5\text{ cm}^2\)