Question

7.3.9.c a semicircle is cut from a square piece of wood. if the radius of the semicircle is 4 in, what is the area of the semicircle?

Explanation:

Step1: Recall the formula for the area of a circle

The area of a full circle is given by the formula \( A = \pi r^2 \), where \( r \) is the radius of the circle.

Step2: Derive the formula for the area of a semicircle

A semicircle is half of a full circle, so the area of a semicircle (\( A_{semicircle} \)) will be half of the area of the corresponding full circle. Therefore, the formula for the area of a semicircle is \( A_{semicircle} = \frac{1}{2} \pi r^2 \).

Step3: Substitute the given radius into the formula

We are given that the radius \( r = 4 \) inches. Substituting \( r = 4 \) into the formula for the area of a semicircle, we get:

$$
LATEXBLOCK0
$$

If we use \( \pi \approx 3.14 \), then:

$$ A_{semicircle} \approx 8 \times 3.14 = 25.12 $$

Answer:

The area of the semicircle is \( 8\pi \) square inches (or approximately \( 25.12 \) square inches).