Question

the radius of a semicircle is 1 foot. what is the semicircles area? round your answer to the nearest hundredth. square feet

Explanation:

Step1: Recall the formula for the area of a full 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: Determine the formula for the area of a semicircle.

A semicircle is half of a full circle, so the area of a semicircle (\( A_{semicircle} \)) is half the area of the full circle. Thus, 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 \( r = 1 \) ft. Substituting \( r = 1 \) into the formula for the area of a semicircle, we get:
\( A_{semicircle} = \frac{1}{2} \pi (1)^2 \)

Step4: Simplify the expression.

Simplifying \( \frac{1}{2} \pi (1)^2 \), we have \( \frac{1}{2} \pi (1) = \frac{\pi}{2} \).

Step5: Calculate the numerical value and round to the nearest hundredth.

Using the approximation \( \pi \approx 3.14159 \), we calculate \( \frac{\pi}{2} \approx \frac{3.14159}{2} \approx 1.570795 \). Rounding this to the nearest hundredth gives \( 1.57 \).

Answer:

\( 1.57 \) square feet