Question

determine the shaded area.

the shaded area is \\(7.37\\) \\(\text{in.}^2\\).
(type an integer or decimal rounded to the nearest hundredth as needed.)

Explanation:

Identify the given dimensions

Using the Area of Semicircle knowledge point

• Outer semicircle diameter: \(D = 5\text{ in.}\)
• Inner semicircle diameter: \(d = 2.5\text{ in.}\)
• Outer radius: \(R = \frac{5}{2} = 2.5\text{ in.}\)
• Inner radius: \(r = \frac{2.5}{2} = 1.25\text{ in.}\)

Calculate the outer semicircle area

Using the Area of Semicircle knowledge point

$$ A_{\text{outer}} = \frac{1}{2} \pi R^2 = \frac{1}{2} \pi (2.5)^2 = 3.125\pi \approx 9.8175\text{ in.}^2 $$

Calculate the inner semicircle area

Using the Area of Semicircle knowledge point

$$ A_{\text{inner}} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (1.25)^2 = 0.78125\pi \approx 2.4544\text{ in.}^2 $$

Calculate the shaded area

Using the Shaded Area knowledge point

$$ A_{\text{shaded}} = A_{\text{outer}} - A_{\text{inner}} = 3.125\pi - 0.78125\pi = 2.34375\pi \approx 7.3631\text{ in.}^2 $$

Round to the nearest hundredth

Using the Shaded Area knowledge point

$$ A_{\text{shaded}} \approx 7.36\text{ in.}^2 $$

Answer:

Determine the shaded area.

The shaded area is <blank>\(7.36\)</blank> <blank>\(\text{in.}^2\)</blank>.
(Type an integer or decimal rounded to the nearest hundredth as needed.)